Calculus

As a calculus instructor, I prepared these PDFs as a review of the chapters in Stewart’s “Single Variable Calculus, Early Transcendentals.” It includes example problems which have been worked out in some detail. I hope you find these useful.

2.1 Tangent and Velocity Problems

2.2 Limit of a Function

2.3 Calculating Limits Using the Limit Laws

2.4 Precise Definition of a Limit

2.5 Continuity

2.6 Limits at Infinity Horizontal Asymptotes

2.7 Derivatives and Rates of Change

2.8 Derivative as a Function

3.1 Derivatives of Polynomials and Exponential Functions

3.2 Product and Quotient Rules

3.3 Derivatives of Trigonometric Functions

3.4 Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Logarithmic Functions

3.9 Related Rates

3.10 Linear Approximations and Differentials

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 How Derivatives Affect the Shape of a Graph

4.4 Intermediate Forms & LHospitals Rule

4.5 Curve Sketching

4.7 Optimization Problems

4.8 Newtons Method

4.9 Antiderivatives

5.1 Riemann Sums and Distances

5.2 Definite Integral

5.3 Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Net Change Theorem

5.5 Substitution Rule

6.1 Areas Between Curves

6.2 Volumes

6.3 Volumes by Cylindrical Shells

6.5 Average Value of a Function

7.1 IBPs

7.2 Trigonometric Integrals

7.3 Trigonometric Subst

7.4 IBPFs

7.5 Integration Strategies

7.7 Approximate Integration

7.8 Improper Integrals

8.1 Arc Length

8.2 Surface Revolution

8.3 Physics Engineering

9.1 Modeling Differential Eqs

9.2 Direction Fields Euler Method

9.3 Separable Equations

9.4 Population Growth Models

9.5 Linear Equations

9.6 Predator Prey

10.1 Parametric Equation Curves

10.2 Parametric Curves

10.3 Polar Coordinates

10.4 Polar Area Lengths

10.5 Conic Sections

11.1 Sequences

11.2 Series

11.3 Integral Test Sum Estimates

11.4 Comparison Test

11.5 Alternating Test

11.6 Absolute Ratio Root Test

11.7 Testing Series Convergence Strategy

11.8 Power Series

11.9 Functions as Power Series

11.10 Taylor Maclaurin Series

12.1 3D Coordinates

12.2 Vectors

12.3 Dot Product

12.4 Cross Product

12.5 Equations for Lines Planes