Course overview (MAT 265: Calculus for Engineers I at Arizona State University)

1.3 Graphical and Tabular Limits

1.4 Algebraic Limits

1.5 Continuity

1.6 Limits at Infinity

2.1 Derivatives and Rates of Change

2.2 Derivatives with Limits

2.3 The Power Rule, Tangent Lines, and Normal Lines

2.4 The Product and Quotient Rule

2.5 The Chain Rule

2.6 Implicit Differentiation

2.7 Related Rates

2.8 Linearization and Linear Approximation

3.1 Exponential Functions

3.2 Inverse Functions, Limits of Logarithmic and Exponential Functions

3.3 Derivatives of Logarithmic and Exponential Functions

3.5 Derivatives of Inverse Trigonometric Functions

3.7 Indeterminate Forms and L'Hôpital's Rule

4.1 Absolute Extrema

4.2 The Mean Value Theorem

4.3 Derivatives and Shapes of Graphs

4.4 Curve Sketching

4.5 Optimization Techniques

4.7 Antiderivatives

5.1 Areas and the Riemann Sum

5.2 The Definite Integral

5.3 Evaluating Definite Integrals

5.4 The Fundamental Theorem of Calculus

4.7 Antiderivatives

5.2 The Definite Integral

5.3 Evaluating Definite Integrals

5.5 The Substitution Method

6.1 Integration by Parts

6.2 Trigonometric Substitution

6.3 Partial Fraction Decomposition

6.4 Integration with Tables

6.5 Simpson's Rule and Trapezoid Rule

6.6 Improper Integrals

7.1 Areas Between Curves

7.2 Disk/Washer Method for Solids of Revolution

7.3 Shell Method for Solids of Revolution

7.4 Arc Length

7.6 Work (Physics Application)

8.1 Sequences

8.2 Series

8.3 Special Series (Bonus Lecture)

8.4 Ratio Test for Convergence

8.5 Interval and Radius of Convergence for Power Series

8.6 Representing Functions as Power Series

8.7 MacLaurin and Taylor Series

9.1 Parametric Curves

9.2 Calculus with Parametric Curves

9.3 Polar Coordinates

9.4 Calculus in Polar Coordinates