Columbia University major

1. Engineering Mechanics
Minor: Entrepreneurship and Innovation

2. Major Definition
• the science of mechanics and its applications to various engineering
disciplines
• frequently referred to as applied mechanics, it includes the study of
the mechanical and other properties of materials, stress analysis of
stationary and movable structures, the dynamics and vibrations of
complex structures, aero- and hydrodynamics, and the mechanics of
biological systems.

3. Current Columbia research that interests me
• Flight structures: composite materials, smart and multifunctional
structures, multiscale and failure analysis, vibration control, computational
mechanics and finite element analysis, fluid-structure interaction,
aeroelasticity, optimal design, and environmental degradation of
structures.
• Columbia is involved with: The Institute of Flight Structures
• The Institute of Flight Structures was established within the Department of Civil
Engineering and Engineering Mechanics through a grant from the Daniel and
Florence Guggenheim Foundation. The institute provides graduate training in
aerospace and aeronautical-related applications of structural analysis and design.

4. After college
• Major areas where civil engineers work include transportation, buildings, bridges,
stadiums, dams, tunnels, water-supply, aerospace, the automotive industry, and
the power industry.
• Consulting Industry: Involved with the design of the infrastructure.
• Federal/State/Local Government: Helping to design and build structures that the public
needs such as bridges, roads, tunnels, and airports.
• Construction: Primarily overseeing construction projects in the private industry to ensure
safety and efficiency within the design specifications.
• Academia: Teaching in colleges and universities or conducting research.
• Research Firms or Laboratories: Primarily conducting field research and data collection as a
function of consultation, laboratory services, and field technician services.
• Organizations that recruit at Columbia include Arup, HNTB, Parsons, Gannett Fleming, Lend
Lease, Skanska, Boeing, Thornton Tomasetti, STV, The Port Authority of NY & NJ, Turner
Construction Co., and many others.

5. Semester III
Calc IV: Multiple integrals, Taylor's formula in several variables, line and
surface integrals, calculus of vector fields, Fourier series.
Physics Lab: Intro to experimental physics
HAVE TO TAKE FOR ALL ENGINEERING MAJORS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Engineering Mechanics: Prerequisites: PHYS C1401 and MATH V1101-
V1102 and V1201. Elements of statics; dynamics of a particle and
systems of particles; dynamics of rigid bodies.
MATLAB (Could take over summer depending on advisor meeting)

6. Semester IV – I want to study abroad
• Ordinary Differential Equations
• Columbia Core “GLOBAL CORE” courses

7. Semester V
• Mechanics of solids: Stress and strain. Mechanical properties of materials. Axial load,
bending, shear and torsion. Stress transformation. Deflection of beams. Buckling of
columns. Combined loadings. Thermal stresses.
• Fluid mechanics: Fluid statics. Fundamental principles and concepts of flow analysis.
Differential and finite control volume approach to flow analysis. Dimensional analysis.
Application of flow analysis: flow in pipes, external flow, flow in open channels.
• Applied math I:LINEAR ALGEBRA Matrix algebra, elementary matrices, inverses, rank,
determinants. Computational aspects of solving systems of linear equations: existence-
uniqueness of solutions, Gaussian elimination, scaling, ill-conditioned systems, iterative
techniques. Vector spaces, bases, dimension. Eigenvalue problems, diagonalization,
inner products, unitary matrices.
• Dynamics and vibrations: Prerequisites: MATH V1201. Corequisites: ENME E3105.
Kinematics of rigid bodies; momentum and energy methods; vibrations of discrete and
continuous systems; eigen-value problems, natural frequencies and modes. Basics of
computer simulation of dynamics problems using MATLAB or Mathematica.

8. Semester VI
• Experimental mechanics: Material behavior and constitutive relations.
Mechanical properties of metals and cement composites. Structural
materials. Modern construction materials. Experimental investigation of
material properties and behavior of structural elements including fracture,
fatigue, bending, torsion, buckling.
• Structural analysis: Trusses, arches, cables, frames; influence lines;
deflections; force method; displacement method; computer applications.
• Applied math II: Partial differential equations of engineering in rectangular,
cylindrical, and spherical coordinates. Separation of the variables.
Characteristic-value problems. Bessel functions, Legendre polynomials,
other orthogonal functions; their use in boundary value problems.
Illustrative examples from the fields of electromagnetic theory, vibrations,
heat flow, and fluid mechanics.

9. Semester VII
• Finite elements: Focus on formulation and application of the finite
element method to engineering problems such as stress analysis,
heat transfer, fluid flow and electromagnetics.
• Advanced solids: Stress and deformation formulation in two-and
three-dimensional solids; viscoelastic and plastic material in one and
two dimensions energy methods.
• Theory of vibrations: Frequencies and modes of discrete and
continuous elastic systems. Forced vibrations-steady-state and
transient motion. Effect of damping. Exact and approximate methods.
Applications.

10. Semester VIII
• Advanced mechanics- Differentiation of vector functions. Review of
kinematics. Generalized coordinates and constraint equations.
Generalized forces. Lagrange's equations. Impulsive forces. Collisions.
Hamiltonian. Hamilton's principle.

11. Extra courses:
FOR FUN:
• Introduction to Human Spaceflight
• Theory of the Universe
FOR MY MINOR:
• Intro to accounting and finance
• Managing technological innovation
• Global entrepreneurship in civil engineering
• Program and problem solving
• Design and agile project management