Engineering mathematics
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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$1,162 · Engineering mathematics · 18 tutoring hrs
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Topics typically covered
Standard syllabus
Vector calculus
- Vectors in R³; dot and cross products
- Vector-valued functions; arc length and curvature
- Partial derivatives and the gradient
- Directional derivatives and tangent planes
- Chain rule for multivariable functions
Multiple integration and vector fields
- Double and triple integrals; change of variables
- Line integrals and work; conservative fields
- Green's theorem in the plane
- Surface integrals and flux
- Divergence theorem and Stokes' theorem (statements and applications)
Differential equations for engineers
- First- and second-order linear ODEs (review and extension)
- Systems of ODEs and matrix exponential (introduction)
- Laplace transforms for engineering IVPs
- Fourier series for periodic forcing functions
- Introduction to PDEs: heat and wave equations (overview)
STEM / applied
Applications in engineering disciplines
- Fluid flow: velocity fields, divergence, and curl
- Electromagnetism: Maxwell's equations in integral form (overview)
- Heat transfer and diffusion models
- Vibrations and modal analysis in mechanical systems
- Control systems: transfer functions and stability (introduction)
Computation and laboratory work
- MATLAB or similar for vector calculus visualization
- Numerical solution of ODEs and systems
- Finite-difference approximations for PDEs (introduction)
- Engineering units, dimensional consistency, and interpretation
- Design problems integrating calculus and DE methods
Notes
Topics reflect common engineering mathematics syllabi at US universities, often aligned with a two-course sequence spanning multivariable calculus and differential equations for engineers.