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Midterm
1. Mathematical induction
  • Number systems and elementary functions
  • Mathematical induction
2. Limits and Continuity
  • Limits (An Intuitive Approach)
  • Computing Limits - Limits at Infinity
  • Limits of Trigonometric Functions
  • Continuity
3. Differentiation
  • Tangent Lines and Rates of Change
  • The Derivative - Techniques of Differentiation
  • Derivatives of Trigonometric Functions
  • The Chain Rule - Implicit Differentiation
  • Derivatives of Inverse Trigonometric Functions
  • Derivatives of Logarithmic and Exponential Functions
  • Derivatives of Hyperbolic Functions
  • Higher Derivatives
  • Linear Approximations

4. Applications of Differentiation
  • Related Rates
  • L’Hopital’s Rule; Indeterminate Forms
  • Intervals of Increase and Decrease; Concavity
  • Relative Extrema; First and Second Derivative Tests
  • Graphs of Polynomials and Rational Functions
  • Maximum and Minimum Values of a Function
  • Applied Maximum and Minimum Problems
  • Rolle’s Theorem; Mean Value Theorem
5. Integration
  • Antiderivatives; The Indefinite Integral
  • Integration by Substitution
  • The Definite Integral
  • The Fundamental Theorem of Calculus
1. Mathematical induction
  • Number systems and elementary functions
  • Mathematical induction
2. Limits and Continuity
  • Limits (An Intuitive Approach)
  • Computing Limits - Limits at Infinity
  • Limits of Trigonometric Functions
  • Continuity
3. Differentiation
  • Tangent Lines and Rates of Change
  • The Derivative - Techniques of Differentiation
  • Derivatives of Trigonometric Functions
  • The Chain Rule - Implicit Differentiation
  • Derivatives of Inverse Trigonometric Functions
  • Derivatives of Logarithmic and Exponential Functions
  • Derivatives of Hyperbolic Functions
  • Higher Derivatives
  • Linear Approximations

4. Applications of Differentiation
  • Related Rates
  • L’Hopital’s Rule; Indeterminate Forms
  • Intervals of Increase and Decrease; Concavity
  • Relative Extrema; First and Second Derivative Tests
  • Graphs of Polynomials and Rational Functions
  • Maximum and Minimum Values of a Function
  • Applied Maximum and Minimum Problems
  • Rolle’s Theorem; Mean Value Theorem
5. Integration
  • Antiderivatives; The Indefinite Integral
  • Integration by Substitution
  • The Definite Integral
  • The Fundamental Theorem of Calculus

6. Applications of Definite Integral

  • Area Between Two Curves
  • Volumes by Slicing; Disks and Washers
  • Volumes by Cylindrical Shells
  • Length of a Plane Curve

7. Techniques of Integration

  • Integration by Parts
  • Trigonometric Integrals
  • Trigonometric Substitutions
  • Integrating Rational Functions by Partial Fractions
  • Numerical Integration
  • Improper Integrals

8. Infinite Series

  • Sequence
  • Infinite Series
  • Convergence Tests
  • Taylor’s Theorem for Basic Functions

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