Calculus

Took this course twice, once at Marianopolis College and again at Waterloo.

Link to course notes (MATH117) here. Taken in 1A SE. Link to course notes (MATH119) here. Taken in 1B SE.

• Functions
• Limits
• Continuity
• Fundamental Theorem of Calculus

Differential Calculus

• Derivatives
• Related Rates
• Linear Approximation
• Differentials
• Integrals
• Optimization

Differential Calculus Theorems

These theorems apply to continuous functions.

• Differentiability Implies Continuity
• Mean Value Theorem
• Extreme Value Theorem
• Intermediate Value Theorem
• L’Hopital’s Rule

Integral Calculus

• Integrals
• Volumes of Solids of Revolution

Multivariate Calculus

• Multivariate Function
• Multivariate Limits
• Partial Derivatives
• Parametric Equation
• Differentials
• Method of Lagrange
• Directional Derivatives
• Gradient Vector
• Double Integrals
• Coordinate System
• Change-of-Variable Formula

Midterm topics that I struggle with

• Parametric Equation
• Directional Derivatives (almost there, we are there to master it)
• Method of Lagrange

Taylor Polynomials and Series

• Root Finding
• Interpolation
• Taylor Polynomials
• Series
• Big O