Lecture Notes (PDF)

Below are the lecture note PDF files that you need to print out and bring with you to class each week.

Notes: Integration Rules (I)

• I3: Substitution Rule for Indefinite Integrals

• I4: Substitution Rule for Definite Integrals

• I5: Integration By Parts for Indefinite Integrals

• I6: Integration By Parts for Definite Integrals

Notes: Advanced Integration Techniques (AI)

• AI1: Trigonometric Integrals (Odd Powers Sine and Cosine)

• AI2: Trigonometric Integrals (Even Powers Sine and Cosine)

• AI3: Trigonometric Integrals (Powers of Secant and Tangent)

• AI4 and AI5: Trigonometric Substitutions

• AI6 Partial Fractions

• AI7 Integrating Partial Fractions

• AI8 Improper Integrals

• AI9 p-form Improper Integrals

Notes: Applications of Definite Integrals (AD)

• AD1: Area Between Two Curves

• AD2: Volume of a Solid of Revolution

• AD3: Arc Length

Notes: Parametric Equations (PE)

• PE1: Parametric Curves

• PE2: Eliminating Parameters

• PE3: Derivatives and Parametric Curves

• PE4: Length of Parametric Curves

Notes: Polar Coordinates (PC)

• PC1: Polar Coordinates

• PC2: Polar Regions

• PC3: Polar Curves

Notes: Introduction to Series (S)

• S1: Sequences

• S2: Limits of Sequences

• S3: Series

• S4: Geometric Series

• S3: p-Series

Notes: Series Testing (ST)

• ST1: Divergence Test

• ST2: Integral Test

• ST3: Direct Comparison Test

• ST4: Limit Comparison Test

• ST5: Alternating Series Test

• ST6: Ratio Test

• ST7: Root Test

• ST8: Absolute Convergence

Notes: Power Series (PS)

• PS1 and PS2 Power Series

• PS3 Power Series Representation

• PS4 Power Series Calculus

• PS5 Taylor and Maclaurin Series

• PS6 Special Maclaurin Series