Calculus 2

1: Limits, Continuity, Sequences & Series: §

• Limit
  • Limit Laws
  • Standard Limits
  • Formal Definition Of A Limit
  • Sandwich Theorem
• Continuity
  • Differentiability
  • L’Hôpital’s Rule
  • Derivation By First Principles
• Sequence
  • Factorial
• Series
  • Geometric Series
  • P-Harmonic Series
  • Comparison Test
  • Divergence Test
  • Ratio Test

2: Hyperbolic Functions §

• Hyperbolic Function
• Addition & Double Angle Formulae
• Trigonometric & Hyperbolic Identities
• Derivatives & Antiderivatives of Hyperbolic Functions

3: Complex Numbers §

• Complex Number
• De Moivre’s Theorem
• Connecting Trigonometric Functions With Hyperbolic Functions Using Complex Numbers
• Differentiating & Integrating Trigonometric Functions Using Complex Numbers

4: Integral Calculus §

• Integration By Substitution
• Integration By Parts
• Trigonometric & Hyperbolic Substitution
• Partial Fraction Decomposition

5: First Order ODEs §

• Differential Equations
• Order (Differentials)
• Ordinary Differential Equation
  • Separable ODEs
  • Linear First Order ODE
• Simplifying First Order ODEs via substitution
• Qualitative Analysis
• Population Models
• Mixing Problem

6: Second Order ODEs §

• Second Order Linear ODE
• Second Order Linear ODEs (Constant Coefficients)
  • Second Order Linear Homogenous Equation (Constant Coefficients)
  • Second Order Linear Inhomogeneous Equation (Constant Coefficients)
• Modelling Springs with Differential Equations

7: Functions of Two Variables (Bivariate/Binary Functions) §

• Bivariate Function
• Plane
• Graphing a Bivariate Function
• Limits and Continuity of Bivariate Functions
• Partial Derivative
• Tangent Plane
  • Differentiability of a Bivariate Function
• Partial Differential Equation
• Second Order PDE
• Directional Derivative
• Gradient Vector
• Second Derivative Test
• Double Integral