Classical thermodynamics of a general reactive system; conservation of energy and principles of increase of entropy; fundamental relation of thermodynamics; Legendre transformations; phase transitions and critical phenomena; equilibrium and stability criteria in different representation; irreversible thermodynamics. Introduction to statistical thermodynamics.

Prerequisite: MAE 302; MA 401 or MA 511

Typically offered in Spring only

Gas-phase thermochemistry including chemical equilibrium and introductory chemical kinetics. Homogeneous reaction phenomena. Subsonic and supersonic combustion waves in premixed reactants (deflagration and detonation). Effects of turbulence. Introduction to diffusion flame theory.

Prerequisite: MAE 201 or MAE 252 or MAE 308

Typically offered in Fall only

Development of basic equations for steady and transient heat and mass transfer processes. Emphasis on application of basic equations to engineering problems in areas of conduction, convection, mass transfer and thermal radiation.

Prerequisite: MAE 310

Typically offered in Fall only

This course will cover topics related to automotive power systems. In particular, this course provides fundamental concepts and knowledge on different power station options for automotive applications including internal combustion engines, battery electrical vehicles, engine/battery hybrid vehicles, and fuel cell powered vehicles.

P: Graduate Standing

Typically offered in Spring only

Basic topics in advanced dynamics and with applications to aerospace systems. Rotating coordinate systems, Euler angles, three-dimensional kinematics and kinetics, angular momentum methods and an introduction to analytical mechanics. Examples are concentrated in the area of aerospace vehicles, but the methods learned will be applicable to land-based vehicles and any engineering system undergoing rigid body rotation, e.g. wind turbines, biomechanical systems, machine tools, robotic systems, etc.

Prerequisite: (MAE 208 or PY 205) and MA 242 and (MA 301 or MA 341)

Typically offered in Fall and Summer

Principles of structural vibration beginning from single and multi-degree of freedom systems and extending to distributed systems. Forced system response, vibration of strings, bars, shafts and beams and an introduction to approximate methods.

Prerequisite: MAE 315

Typically offered in Fall only

This course covers advanced materials related to mathematical models and designs in automotive vehicles as multiple degrees of freedom systems for dynamic behaviors in acceleration, braking, rollover, aerodynamics, suspections, tire, and drive train.

Prerequisite: MAE 208 or MAE 315 or MAE 472 or equivalent; or consent of the instructor

Typically offered in Spring only

This is a graduate level course designed for graduate students and undergraduate seniors. This course examines precision issues for products, manufacturing machines, processes, and instruments. Modern manufacturing technologies are distinct in their multifarious nature in product sizes, materials, energy forms, theories, and information types; however, the key to their success relies on the management of precision. This course discusses issues critical to both existing precision manufacturing and future sub-micron/nano technology. Important topics include fundamental mechanical accuracies; manufacturing systems and processes; geometric dimensioning and tolerancing; process planning, tolerance charts, and statistical process control; principles of accuracy, repeatability, and resolution; error assessment and calibration; error budget; reversal principles; joint design and stiffness consideration; precision sensing and control; precision laser material processing.

Prerequisite: MAE 496 or MAE 415 or equivalent or instructor permission

Typically offered in Fall only

Introduction to principles of acoustic radiation from vibrating bodies and their related fields. The radiation of simple sources, propagation of sound waves in confined spaces and transmission through different media.

Prerequisite: MA 301 and MAE 308 or MAE 356

Typically offered in Fall and Spring

Topics in movement biomechanics and computational analyses of movement, including muscle physiology and mechanics, advanced muscle modeling, neural control of muscle and motor control theories, and dynamic simulation and optimization. Discussion of fundamental research underpinnings and clinical and sports applications.

P: MAE208 or equivalent

Typically offered in Fall only

Linear Multivariable control and design for multibody engineering systems (robotics) and aircraft controls and navigation. Emphasis on multi-input and multi-output (MIMO) system analysis and design using frequency-based approach. Controllability andobservability, transmission zeroes and pole-zero cancellation, eigenstructures, singular value decomposition in frequency domain, stability and performance robustness of MIMO systems.

Prerequisite: MAE 435, MA 341

Typically offered in Spring only

Nonlinear system analysis, Lyapunov stability theory, absolute stability, feedback linearization, sliding mode control, backstepping control technique, as well as various advanced nonlinear control methods.

Prerequisite: MAE 521 or equivalent

Preliminary analysis and design of flight control systems to include autopilots and stability augmentation systems. Study of effects of inertial cross-coupling and nonrigid bodies on vehicle dynamics.

Prerequisite: MAE 457

Typically offered in Fall only

Many think of design as more of an art than a science. However, the growing body of research in the engineering design community teaches us ways to navigate the design of consumer products using interdisciplinary design tools and rational decision making. This course introduces students to scientific design techniques that are more effective than "ad hoc" tactics. By exploring how engineering principles integrate with "real world" design challenges, students will learn to solve product design problems that encompass heterogeneous markets, multiple disciplines, and large-scale complex systems.

Prerequisite: MA 241

Typically offered in Spring and Summer

Application of engineering methods to experimental flight testing of fixed-wing aircraft for determination of performance and handling qualities of air vehicles. Risk minimization techniques are included in the formulation of a flight test plan. Collected flight test data is corrected for standard day and analyzed.

Prerequisite: Graduate standing, Aerospace Engineering Majors, MAE 525

Typically offered in Spring only

Nonlinear optimization techniques with applications in various aspects of engineering design. Terminology, problem formulation, single and multiple design variables, constraints, classical and heuristic approaches, single and multiobjective problems, response surface modeling, and tradeoffs in complex engineering systems. Numerical optimization algorithms and implementation of these optimization techniques. Graduate standing in engineering recommended.

Prerequisite: Graduate standing in Engineering is recommended.

Typically offered in Fall only

This course is designed for graduate students who wish to learn fundamentals and applications of smart structures and micro transducers. The course focuses on materials, structures, design, fabrication, and characterization of micro transducers. It also covers the recent progress in applications of micro transducers in aerospace, biomedical, civil, electrical and mechanical engineering.

Prerequisite: MAE 314, MAE 315, or equivalent.

Typically offered in Fall only

Fundamental concepts of the finite element method for linear stress and deformation analysis of mechanical components. Development of truss, beam, frame, plane stress, plane strain, axisymmetric and solid elements. Isoparametric formulations. Introduction to structural dynamics. Practical modeling techniques and use of general-purpose codes for solving practical stress analysis problems.

Prerequisite: MAE 316 or MAE 472

Typically offered in Fall only

Principles of Mechatronics Design, review of logic gates, microprocessor architecture, sensors and actuators, A/D and D/A conversion techniques, real-time multi-tasking programming concepts, direct digital control implementation. "Hands-on" experience through several laboratory assignments and final team project.

Prerequisite: Structured Programming Experience, Senior/Graduate Standing in WPS/MAE.

Typically offered in Spring only

A practical introduction to electromechanical systems with emphasis on modeling, analysis, design, and control techniques. Provides theory and practical tools for the design of electric machines (standard motors, linear actuators, magnetic bearings, etc). Involves some self-directed laboratory work and culuminates in an industrial design project. Topics include Maxwell's equations, electromechanical energy conversion, finite element analysis, design and control techniques.

Prerequisite: MA 341

Typically offered in Spring and Summer

Fundamentals and applications of micro/nano sensors and actuators. Emphasis upon MEMS/NEMS design, microfabrication techniques, and case studies of MEMS devices. Nanomaterials and NEMS devices also covered. Students have opportunity to learn commercial software packages on design and simulation of MEMS and hear from experts from leading MEMS companies through guest lectures. Previous knowledge of MEMS and nanotechnology is not required. The course is restricted to advanced undergrads and graduate students in engineering, materials science, physics and biomedical fields.

Typically offered in Fall only

Manufacturing techniques with emphasis on selection of those producing most favorable end result. Classical plate theory, materials properties and failure theories. Micromechanics, repair, plate solutions and elasticity solutions covered as requiredto meet special interests of students.

Prerequisite: MAE 316 or MAE 472

Typically offered in Spring only

An application-oriented introduction to smart structures and materials with examples from mechanical, aerospace and biomedical engineering. Experimentally observed phenomena, micromechanisms, and models for material behavior. Team work developing simulation tools for typical applications. Validating results experimentally using PC-based data acquisition systems.

Prerequisite: MAE 415 or MAE 472

Typically offered in Spring only

Introduces production/structure/property/function relation and application of a number of materials mainly for biomedical, mechanical and aerospace applications. Topics include ultra light materials (production, processing and applications of cellular solids), biomaterials (classes and application of materials in medicine and dentistry), composites (classes and application), refractory materials and coatings for high temperature applications, thin film shape memory alloys for micro-electro mechanical systems (MEMS).

Prerequisite: MSE 201 and MAE 314

Typically offered in Fall only

Psychrometric process representations. Heating and cooling coil design. Heat pump design. Air washer design. Direct contact heat and mass transfer systems. Ventilation requirements, air dilution calculations. Cooling load calculations; CLTD, CLF andtransfer functions methods. Room air distribution.

Prerequisite: MAE 403, 404

Typically offered in Spring only

Development of principles of advanced strength of materials and elasticity theory leading to solution of practical engineering problems concerned with stress and deformation analysis. Tensor analysis, coordinate transformations, alternative measures of strain, elastic constitutive equations, stress measures, formulation and solution of two and three dimensional elasticity problems. Examples include advanced beam theory for shear deformation and large deformation, contact mechanics, stress concentration, pressure vessels and compound cylinders, thermal stress analysis, and stresses in layered microelectronic devices.

Prerequisite: MAE 316

Typically offered in Fall only

Concept of elastic stress intensity factor, Griffith energy balance, determination of the elastic field at a sharp crack tip via eigenfunction expansion methods, J integrals analysis, experimental determination of fracture toughness, fatigue crack growth, elastic-plastic crack tip fields. Emphasis on modern numerical methods for determination of stress intensity factors, critical crack sizes and fatigue crack propagation rate predictions.

Prerequisite: MAE 316

Typically offered in Spring and Summer

Real-time programming for servo control using an embedded controller. Software and hardware interfacing for control of a D.C. servo device. Introduction of multi-tasking to establish concurrent control of several processes, transforming servo loop into a process executing concurrently on single board computer. Provision for hands-on development systems and software emulators.

Prerequisite: Pascal, C, FORTRAN or Assembly language experience

Foundations of dimensional metrology and error analysis as applied to accuracy and repeatability in machine design. Plane, length, angle, and roundness metrology. Design of precision systems, Abbe' principle, error analysis, measurement, and compensation. Precision instruments and operating principles. Hands-on experience with measurement instruments and techniques.

Prerequisite: Senior standing in MAE or BS in other curriculum

Typically offered in Spring only

Use of optical fiber and other photonic device based sensors to measure strain, temperature and other measurands in aerospace, mechanical, civil and biomedical applications. An introduction to optical waveguide analysis will be provided at the beginning of the course.

Prerequisite: MAE 371 or MAE 316

Typically offered in Fall only

This course is offered alternate odd years

Review of basic thermodynamics pertinent to gas dynamics. Detailed development of general equations governing fluid motion in both differential and integral forms. Simplification of the equations to those for specialized flow regimes. Similarity parameters. Applications to simple problems in various flow regimes.

Prerequisite: MAE 201 or MAE 252 or MAE 308

Typically offered in Fall and Summer

Development of fundamental aerodynamic theory. Emphasis upon mathematical analysis and derivation of equations of motion, airfoil theory and comparison with experimental results. Introduction to super sonic flow theory.

Prerequisite: MAE 252

This course educates graduate students in the design of experiments and basis for model testing and scaling laws; uncertainty and error analysis in selecting measurement systems for experiments; qualitative and quantitative technologies for obtaining measurements; analysis, post-processing and visualization techniques of data.

Prerequisite: MAE 308 and MAE 451 or equivalent

Typically offered in Spring only

Equations of motion in supersonic flow; unsteady wave motion, velocity potential equation; linearized flow; conical flow. Slender body theory. Methods of characteristics. Shockwave/ boundary layer interactions.

Prerequisite: MAE 351 or MAE 550

Typically offered in Spring only

Fundamentals of inviscid and viscous hypersonic flowfields. Classical and modern techniques for calculating shock wave shapes, expansions, surface pressures, heat transfer and skin friction. Applications to high speed aircraft, rockets and spacecraft.

Prerequisite: MAE 553

This course covers the principles for acoustic and elastic propagation in fluids and solids. Diffraction theory is developed for finite sources. The notions of wavepacket, dispersion and waveguiding are reviewed. The fundamentals of the theory of elasticity and elastic propagation in solids are introduced, based on tensor analysis. Time reversal of acoustic waves is presented, as well as applications to underwater acoustics, medical imaging and therapy, nondestructive testing, elasticity imaging.

Typically offered in Spring only

Macroscale fluid mechanics, heat and mass transfer. Theories of microfluidics and nanofluidics. Applications in mechanical, biomedical, and chemical engineering. Discussions of journal articles and modern fluid dynamics projects. Expert guest lectures on advanced micro/nanotechnology topics.

Prerequisite: MAE 310 and MA 427

Typically offered in Spring only

Introduction to integration of the governing partial differential equations of fluid flow and heat transfer by numerical finite difference and finite volume means. Methods for parabolic, hyper-bolic and elliptical equations and application to model equations. Error analysis and physical considerations.

Prerequisite: MA 501 or MA 512, MAE 550 or MAE 557, proficiency in the FORTRAN programming language is required

Typically offered in Fall only

Discussion of inviscid flow fields over wings in subsonic flow. Vortex lattice methods, lifting surface theories and panel methods developed for wings with attached flow and leading-edge separation. Calculation of aerodynamic characteristics and determination of effects of planform and airfoil shapes.

Prerequisite: MAE 551

Typically offered in Spring only

This course is offered alternate years

Introduction to kinetic theory, statistical mechanics and chemical thermodynamics. Law of Action. Vibrational and chemical rate processes. Application to equilibrium and nonequilibrium flows.

Prerequisite: MAE 550

Typically offered in Fall only

This course will cover topics related to space exploration systems. In particular, the basic concepts of orbital mechanics needed for space mission planning will be covered, along with the essential subsystems found on a typical spacecraft.

Prerequisite: MAE 467 Introduction to Space Flight or Graduate Standing and Consent of Instructor

Typically offered in Fall only

Conceptual framework and development of hydrodynamic stability theory. Application of the theory to two-dimensional incompressible and compressible subsonic, transonic, supersonic and hypersonic flows. Results for three-dimensional flows. Introduction of mechanisms of transition and discussion of transition models in numerical methods.

Prerequisite: MAE 550

Typically offered in Spring only

This course is offered alternate years

The course will focus on non-turbomachinery, air-breathing hypersonic aeropropulsion applications. Specific propulsion systems to be covered include ramjets and scramjets, pulsed detonation engines, and combined cycle engines, with historical perspective.

Prerequisite: Both MAE 458 and MAE 459 or both MAE 302 and MAE 308

Modeling and simulation of two-phase flows using interface tracking approach and ensemble averaging approaches. Model validation and verification based on interface-tracking data, boiling models. Nuclear reactor applications. The course focuses on interface tracking methods understanding as applied to bubbly flow simulations. Students will develop a simplified solver to track 2D bubbles/droplets throughout the course homework assignments and will learn how to apply this approach for better understanding of multi-phase flow as part of the course project.

Typically offered in Spring only

This course is offered alternate odd years

Individual or small group investigation of a problem stemming from a mutual student-faculty interest. Emphasis on providing a situation for exploiting student curiosity.

Typically offered in Fall, Spring, and Summer

Faculty and student discussions of special topics in mechanical engineering.

Prerequisite: Advanced Undergraduate standing or Graduate standing

Typically offered in Fall and Spring

Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain half-time continuous registration to complete incomplete grades, projects, final master's exam, etc.

Prerequisite: Master's student

Typically offered in Summer only

For students in non-thesis master's programs who have completed all credit hour requirements for their degree but need to maintain full-time continuous registration to complete incomplete grades, projects, final master's exam, etc. Students may register for this course a maximum of one semester.

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

For students in non thesis master's programs who have completed all other requirements of the degree except preparing for and taking the final master's exam.

Prerequisite: Master's student

Typically offered in Fall and Spring

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Master's student

Typically offered in Spring only

Thesis Research

Prerequisite: Master's student

Typically offered in Fall, Spring, and Summer

For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.

Prerequisite: Master's student

Typically offered in Summer only

Individual research in the field of mechanical engineering.

Prerequisite: Graduate standing in Mechanical Engineering, Consent of Adviser

Typically offered in Fall, Spring, and Summer

Analysis and establishment of conclusions of classical thermodynamics from the microscopic viewpoint. Topics include: ensemble methods, partition functions, translational, rotational and vibrational energy modes of an ideal gas, chemical equilibrium, imperfect gases, dense fluids, critical-point theories, mean free path concepts, Boltzmann equation, hydrodynamic equations from kinetic theory and properties of disordered composite media.

Prerequisite: MAE 501

Typically offered in Spring only

The course is intended to be an introduction to fundamentals of energy transport and energy conversion concepts from nano to macro scales. The course will cover the state of energy carriers (photons, electrons, and phonons) and their transport characteristics. A focus will be on material properties that dictate energy related processes. The foundational concepts will then be applied to direct energy conversion devices including thermoelectrics and photovoltaics. Finally, the course will cover system analysis of solid-state energy conversion applications.

Typically offered in Spring only

Advanced theory of detonation and deflagration. Ignition criteria. Direct initiation of detonation including blast-wave theory. Transition from deflagration to detonation. Combustion wave structure and stability. Liquid droplet and solid particle combustion.

Prerequisite: MAE 504

Typically offered in Spring only

Comprehensive, unified treatment of methodologies for solving multidimensional transient and steady heat conduction. Approximate and exact methods of solving nonlinear problems, including phase and temperature-dependent thermal properties, nonlinearboundary conditions. Heat conduction in composite media and anisotropic solids. Use of finite integral transform and Green's function techniques.

Prerequisite: MAE 505 or MA 501

Typically offered in Spring only

Advanced topics in steady and transient, natural and forced convective heat transfer for laminar and turbulent flow through conduits and over surfaces. Mass transfer in laminar and turbulent flow. Inclusion of topics on compressible flow with heat and mass transfer.

Prerequisite: MAE 550

Typically offered in Spring only

Comprehensive and unified treatment of basic theories; exact and approximate methods of solution of radiative heat transfer and the interaction of radiation with conductive and convective modes of heat transfer in participating and non-participatingmedia.

Prerequisite: MAE 505

Typically offered in Fall only

Advanced treatment of the theory of sound generation and transmission. Topics include: techniques for solution of the wave equation, radiation from spheres, cylinders and plates, sound propagation in ducts, scattering.

Prerequisite: MAE 518

Typically offered in Spring only

This graduate-level course is intended for engineering graduate students with interests in the simulation of materials and studying their properties at the molecular level using different atomistic simulation techniques. A special focus will be the molecular dynamics simulation method. Students will be taught to build atomic/molecular models, use the open-source LAMMPS software, and process the simulation data. An independent project is required to complete the course to provide hands-on experience on the atomistic simulation techniques.

Restriction: Graduate standing, basic engineering courses on chemistry, heat transfer, thermodynamics, and physics; some experience in coding and coding language. Basic understanding of wave propagation and wave equations

Typically offered in Fall only

This course emphasizes on control design techniques which result in closed-loop systems that are insensitive to modeling errors and which achieve a prespecified level of performance. Robustness margins against model uncertainty. Robust control design techniques based on linear matrix inequalities. Topics include uncertainty modeling, robust stability and performance, H_inf control, convex optimization technique (LMI), mu-analysis and synthesis, computer-aided analysis and control design.

Prerequisite: Graduate standing in Engineering and Applied Mathematics, MAE 521 or ECE 716

Typically offered in Spring only

The principles of fluid mechanics applied to geophysical systems. Special emphasis placed on those features of these systems, such as almost rigid rotation and stable stratification, which produce unique and important effects. The effects of almost rigid rotations on homogeneous and stratified flows examined in detail.

Prerequisite: MAE 501

Typically offered in Fall only

This course is offered alternate years

Principles of fluid mechanics applied to geophysical systems. Special emphasis on role of stable stratification on the flows in these systems. Detailed study of generation, interaction, propagation and dissipation of internal gravity waves. Studyof other geophysically important flows.

Prerequisite: MAE 725 or equivalent

Typically offered in Spring only

This course is offered alternate years

Classical theories of plasticity and solutions pertaining to rate-independent and -dependent deformations modes in metals, geomaterials and concrete. Ductile failure modes, i.e., shear-strain localization and other failure modes associated with large deformation modes. Inelastic wave propagation, crystalline constitutive formulations and computational aspects of quasi-static and dynamic plasticity.

Prerequisite: Grad. course in elasticity or strength of materials

Typically offered in Fall only

This course is offered alternate even years

Presentation of mechanical and metallurgical fundamentals of materials processing by deformation. Principles of metal working, friction, forging, rolling, extrusion, drawing, high energy rate forming, chipless forming techniques, manufacturing system concept in production.

Prerequisite: Six hrs. of solid mechanics and/or materials

Typically offered in Fall only

Advanced treatment of finite element analysis for non-linear mechanics problems, including most recent developments in efficient solution procedures. Plate bending and shell elements, computational plasticity and viscoplastic materials, large deformation formulations, initial stability and buckling, structural vibrations, incompressible elasticity, contact problems, flow in incompressible media, weighted residuals and field problems. Development of efficient algorithms for practical application.

Prerequisite: MAE 533

Typically offered in Spring only

Mechanical design principles important in high volume production using modern automated assembly technology. Production and component design for ease of assembly as dictated by part handling, feeding, orientation, insertion and fastening requirements. Existing product evaluation and redesign for improved assemblage.

Prerequisite: Graduate standing or PBS status in Engineering

Typically offered in Fall only

Advanced computational methods for integrating, by use of finite differences, and finite volume discretizations, non-linear governing equations of fluid flow; the Euler equations and the Navier-Stokes equations. Topics from current literature.

Prerequisite: MAE 560; proficiency in the FORTRAN programming language is required

Typically offered in Spring only

Development of governing equations for chemically and thermally nonequilibrium flows. Numerical formulation with application to planetary entry flows and supersonic combustion. Numerical examples. Computational problems.

Prerequisite: MAE 560, MAE 766

Typically offered in Spring only

Development of basic concepts and governing equations for turbulence and turbulent field motion. Formulations of various correlation tensors and energy spectra for isotropic and nonisotropic turbulence. Introduction to turbulent transport processes,free turbulence, and wall turbulence.

Prerequisite: MAE 550

Typically offered in Spring only

The course will provide the students with in-depth knowledge of technologies in structural health monitoring using smart materials as sensing and actuating elements to interrogate the structures. Damage detection techniques such as wave, impedance, and vibration-based damage detection techniques will be discussed and applied to different types of structures. Advanced signal processing techniques such as wavelet, neural network, principal component analysis will be used to make the damage more quantifiable.

Prerequisite: MAE 541 or MAE 513 or equivalent

Typically offered in Spring only

Faculty and graduate student discussions of advanced topics in contemporary mechanical engineering.

Prerequisite: Graduate standing

Typically offered in Fall and Spring

Faculty and graduate student discussions centered around current research problems and advanced engineering theories.

Typically offered in Fall and Spring

Individual investigation of advanced topics under the direction of member(s) of the graduate faculty.

Typically offered in Spring only

Teaching experience under the mentorship of faculty who assist the student in planning for the teaching assignment, observe and provide feedback to the student during the teaching assignment, and evaluate the student upon completion of the assignment.

Prerequisite: Doctoral student

Typically offered in Fall and Spring

For students who are preparing for and taking written and/or oral preliminary exams.

Prerequisite: Doctoral student

Typically offered in Fall and Spring

Instruction in research and research under the mentorship of a member of the Graduate Faculty.

Prerequisite: Doctoral student

Typically offered in Fall and Spring

Dissertation Research

Prerequisite: Doctoral student

Typically offered in Fall, Spring, and Summer

For graduate students whose programs of work specify no formal course work during a summer session and who will be devoting full time to thesis research.

Prerequisite: Doctoral student

Typically offered in Summer only

For students who have completed all credit hour, full-time enrollment, preliminary examination, and residency requirements for the doctoral degree, and are writing and defending their dissertations.

Typically offered in Fall, Spring, and Summer