Semester 2Year 1 · EvenCore Subject★★★ Moderate
MATH 102

Engineering Mathematics II

Advanced mathematics covering differential equations, vector calculus, and complex analysis.

3Units
14Topics
4Credits
60hLecture hrs
100Max marks
Your Progress
0 / 14 topics
0% complete
Overview
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Why it matters
Differential equations model everything from population growth to circuit behavior to ML gradient descent. Vector calculus powers computer graphics and physics engines. Complex analysis is essential for signal processing.
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Placement relevance
Builds mathematical maturity. Vector calculus appears in graphics programming interviews. Differential equations in ML/AI roles (gradient descent IS solving differential equations). GATE carries ~15 marks.
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Prerequisites for
Control Systems · Signal Processing · Computer Graphics · Machine Learning · Electromagnetic Theory · Quantum Computing
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Recommended books
Higher Engineering Mathematics by B.S. Grewal · Advanced Engineering Mathematics by Erwin Kreyszig · Differential Equations by Shepley L. Ross
Curriculum — 3 Units
U1
Unit 1 · 4 Topics · 0% complete
Differential Equations
⚡ Key Formulae
First Order:dy/dx + Py = Q (Linear form)
Second Order:ay'' + by' + cy = 0 (Characteristic equation: ar² + br + c = 0)
Solution Types:Real roots: e^(r₁x), e^(r₂x); Complex: e^αx(cos βx, sin βx)
First Order Equations
Higher Order Equations
Linear Differential Equations
Applications
U2
Unit 2 · 6 Topics · 0% complete
Vector Calculus
⚡ Key Formulae
Gradient:∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k
Divergence:∇·F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z
Curl:∇×F = det[i j k; ∂/∂x ∂/∂y ∂/∂z; F₁ F₂ F₃]
Vector Fields
Gradient
Divergence
Curl
Line Integrals
Green's Theorem
U3
Unit 3 · 4 Topics · 0% complete
Complex Analysis
⚡ Key Formulae
Euler's Formula:e^(iθ) = cos θ + i sin θ
Cauchy-Riemann:∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x
Residue:∫f(z)dz = 2πi × Σ Residues
Complex Numbers
Analytic Functions
Cauchy's Theorem
Residue Theorem
Previous Year Questions
Unit 12023 · End Semester10 marks
Solve the differential equation: (D² + 4D + 4)y = e^(-2x) using method of undetermined coefficients.
Unit 22023 · End Semester8 marks
Verify Green's theorem for ∫(xy dx + y² dy) where C is the boundary of the square with vertices (0,0), (1,0), (1,1), (0,1).
Exam Strategy
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Master the methods
Each DE type has its method: Variables separable, Linear (IF), Exact (check condition), Bernoulli. First step: identify type. Wrong method = zero marks.
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Show all steps
Partial marks are generous in Math. Even if final answer is wrong, showing correct method earns 60-70%. Never skip steps.
Related Subjects
Semester 1
Engineering Mathematics I
MATH 101
Semester 5
Signals & Systems
CS 501