Calculus §

Took this course twice, once at Marianopolis College and again during Fall 2021 at Waterloo.

Link to course notes (MATH117) here. Link to course notes (MATH119) here.

• 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