**Every Topic in Your Syllabus is Covered 💯**

*(Note: Some professors may go out of order or skip a topic, so feel free to bounce around.)*

- Study Guide (fill this in as you watch the videos!)
- Basic Derivative and Integral Rules (p. 3-5) (7:55)
- Substitution (p. 6-8) (7:42)
- Integration by Parts Overview (p. 9-11) (7:50)
- IBP - Algebraic and Trig / Exponential (ATE) (p. 12-13) (5:27)
- IBP - Algebraic and Log / Inverse Trig (LIA) (p. 14-15) (6:50)
- IBP - Trig and Exponential (Circular Integration) (p. 16-17) (10:44)
- Substitution and IBP in the Same Problem (p. 18) (4:20)

- Study Guide (fill this in as you watch the videos!)
- Trig Integrals Overview (p. 3-4) (5:04)
- Trig Integrals with Powers of Sine and Cosine (p. 5-7) (15:53)
- Trig Integrals with Sine and Cosine with Different Angles (p. 8) (3:28)
- Trig Integrals with Tangent and Secant - TOES (p. 9-11) (11:26)
- Trig Integrals with Tangent and Secant - No TOES (p. 12-13) (11:46)
- Trig Sub Overview (p. 14-15) (10:32)
- Trig Sub and Completing the Square (p. 16) (12:49)

- Practice Exam Questions
- Practice Exam Questions Answer Key
- Trig Integrals with Sine and Cosine Practice Exam Solutions (9:56)
- Trig Integrals with Tangent and Secant - TOES Practice Exam Solutions (10:39)
- Trig Integrals with Tangent and Secant - No TOES Practice Exam Solutions (20:51)
- Trig Sub - Basic Practice Exam Solutions (17:55)
- Trig Sub and Completing the Square Practice Exam Solutions (20:17)

- Study Guide (fill this in as you watch the videos!)
- Partial Fraction Decomposition - Overview (p. 3-5) (11:59)
- Integration with Linear Factors (p. 6-7) (13:58)
- Integration with Irreducible Quadratic Factors (p. 8-9) (12:23)
- Rationalizing Substitution (p. 10) (9:04)
- Deciding the Right Integration Method to Use (p. 11-12) (7:55)

- Study Guide (fill this in as you watch the videos!)
- Quick Review of Limits (p. 3) (3:22)
- L'Hôpital's Rule (p. 4-5) (5:04)
- Growth Rates (How to Skip L'Hôpital's Rule) (p. 6) (5:10)
- Improper Integrals (p. 7-10) (16:42)
- Comparison Theorem for Improper Integrals (p. 11-12) (6:03)
- The Midpoint Rule (p. 13-14) (3:59)
- The Trapezoidal Rule (p. 15-16) (5:08)
- Simpson's Rule (p. 17-18) (6:32)

- Study Guide (fill this in as you watch the videos!)
- Area Between Curves (p. 3-4) (9:58)
- Volume by Cross Sectional Area (p. 5-6) (11:16)
- Solids of Revolution - Disk and Washer Method (p. 7-10) (14:34)
- Solids of Revolution - Shell Method (p. 11-12) (8:00)
- Rotating About Other Axes (p. 13-14) (13:51)
- Which One - Disk or Shell? (p. 15-17) (14:21)

- Study Guide (fill this in as you watch the videos!)
- Review of Differentials (p. 3) (5:16)
- Basic Physics Concepts (p. 4) (7:27)
- Work - Overview (p. 5) (3:46)
- Work Due to Stretching or Compressing a Spring (p. 6-7) (8:48)
- Work Due to Lifting an Object (p. 8-9) (12:45)
- Work Due to Pumping a Fluid (p. 10-12) (20:18)
- Average Value of a Function (p. 13) (3:54)

- Study Guide (fill this in as you watch the videos!)
- Review of Summation Notation (p. 3) (3:59)
- Series - Overview (p. 4-6) (7:06)
- nth Term Test for Divergence (p. 7) (4:12)
- Geometric Series (p. 8-9) (10:01)
- Telescoping Series (p. 10-11) (7:57)
- The Integral Test (p. 12-13) (10:23)
- p-Series (p. 14) (1:50)

- Practice Exam Questions
- Practice Exam Questions Answer Key
- Series Overview Practice Exam Solutions (3:51)
- nth Term Test for Divergence Practice Exam Solutions (2:27)
- Geometric Series Practice Exam Solutions (4:52)
- Telescoping Series Practice Exam Solutions (10:10)
- The Integral Test Practice Exam Solutions (12:26)
- p-Series Practice Exam Solutions (3:38)

- Study Guide (fill this in as you watch the videos!)
- Direct Comparison Test (p. 3-5) (12:41)
- Limit Comparison Test (p. 6-7) (8:39)
- Which One? Direct Comparison Test or Limit Comparison Test? (p. 8-9) (8:47)
- Alternating Series Test (p. 10-11) (12:01)
- Alternating Series Estimation (p. 12-13) (7:38)
- Absolute and Conditional Convergence (p. 14-15) (6:42)

- Practice Exam Questions
- Practice Exam Questions Answer Key
- Direct Comparison Test Practice Exam Solutions (4:35)
- Limit Comparison Test Practice Exam Solutions (6:33)
- Direct Comparison Test vs Limit Comparison Test Practice Exam Solutions (6:49)
- Alternating Series Test Practice Exam Solutions (5:33)
- Alternating Series Estimation Practice Exam Solutions (6:06)
- Absolute and Conditional Convergence Practice Exam Solutions (7:28)

- Study Guide (fill this in as you watch the videos!)
- Taylor & Maclaurin Series (p. 3-6) (13:11)
- Using Known Taylor Series to Find New Series (p. 7) (3:58)
- Taylor Polynomials (p. 8) (4:02)
- Taylor's Inequality (Taylor's Remainder Theorem) (p. 9-10) (11:05)
- Finding Sums Using Taylor Series (p. 11) (4:10)
- Finding Higher Derivatives Using Taylor Series (p. 12-13) (7:04)

- Study Guide (fill this in as you watch the videos!)
- Parametric Equations Overview (p. 3-6) (13:12)
- The First Derivative with Parametric Equations (p. 7-8) (8:19)
- The Second Derivative with Parametric Equations (p. 9) (6:53)
- Area with Parametric Equations (p. 10) (5:24)
- Arc Length with Parametric Equations (p. 11) (5:57)

- Practice Exam Questions
- Practice Exam Questions Answer Key
- Graphing Parametric Equations Practice Exam Solutions (5:30)
- The First Derivative with Parametric Equations Practice Exam Solutions (8:08)
- The Second Derivative with Parametric Equations Practice Exam Solutions (5:23)
- Area & Arc Length with Parametric Equations Practice Exam Solutions (12:18)

- Study Guide (fill this in as you watch the videos!)
- Polar Coordinates Integral and Area Calculator
- How to Go Through This Study Guide (1:01)
- Polar Coordinates Overview (p. 3-4) (6:53)
- Converting Between Polar and Rectangular Coordinates (p. 5-6) (5:56)
- Converting Between Polar and Rectangular Equations (p. 7-8) (4:58)
- Polar Equations and Graphs (p. 9-12) (5:14)
- Graphing Circles in Polar Form (p. 13) (2:14)
- Graphing Cardioids and Limaçons (p. 14-17) (11:16)
- Graphing Roses (p. 18-19) (4:32)
- Area of Polar Curves (p. 20-21) (5:54)
- Area Between Polar Curves (p. 22-24) (23:42)
- Derivatives Involving Polar Curves (p. 25) (5:27)

- Study Guide (fill this in as you watch the videos!)
- 3D Coordinates, Distance, & Spheres (p. 3-6) (14:23)
- Vectors & Basic Operations (p. 7-13) (16:55)
- The Dot Product & Vector Projections (p. 14-17) (13:35)
- Direction Angles & Direction Cosines (p. 18-19) (4:17)
- The Cross Product (p. 20-25) (25:30)
- Applications of the Cross Product - Torque (p. 26) (3:38)

- Practice Exam Questions
- Practice Exam Questions Answer Key
- 3D Coordinates, Distance, & Spheres Practice Exam Solutions (9:57)
- Vectors & Basic Operations Practice Exam Solutions (5:55)
- The Dot Product & Vector Projections Practice Exam Solutions (19:22)
- The Cross Product Practice Exam Solutions (10:21)

- Study Guide (print me!)
- Limits - Overview (p. 3-6) (11:20)
- Evaluating Limits - Overview (p. 7) (5:36)
- Evaluating Limits Algebraically - Piecewise Functions (p. 8) (5:26)
- Evaluating Limits Algebraically - 0/0 Form (p. 9-12) (21:28)
- Evaluating Infinite Limits - Number/0 Form (p. 13) (5:56)
- Evaluating Infinite Limits - Knowing Graphs (p. 14-15) (5:18)
- The Squeeze Theorem (p. 16) (4:42)
- Limits at Infinity and Horizontal Asymptotes (p. 17-23) (23:09)
- Derivative Rules - Overview (p. 24-25) (7:52)
- Product and Quotient Rules (p. 26-27) (12:35)
- The Chain Rule (p. 28-29) (12:27)
- Indeterminate Forms and L'Hôpital's Rule (p. 30-32) (15:02)
- Growth Rates (How to Skip L'Hôpital's Rule) (p. 33) (4:51)
- How to Do Nasty Limits and Skip the Algebra 😈 (p. 34) (4:10)
- Antiderivatives and Indefinite Integrals (p. 35-38) (13:38)
- Substitution (p. 39-42) (16:26)
- My F****ing Variable Didn't Cancel 😵💫🤬😭 (p. 43) (4:23)
- Substitution with Definite Integrals (p. 44-46) (11:52)
- Substitution vs Basic Integration (p. 47-48) (10:54)

- Study Guide (print me!)
- Trig Functions (p. 3) (4:25)
- The Unit Circle (p. 4-7) (17:35)
- Trig Identities (p. 8-9) (7:39)
- Solving Trig Equations and Inequalities (p. 10-11) (16:13)
- Inverse Trig Overview (p. 12-13) (7:46)
- Evaluating Mixed Trig Function Expressions (p. 14-17) (10:47)
- Evaluating Mixed Trig Function Expressions with Variables (p. 18) (3:50)

- Study Guide (print me!)
- Special Products and Factoring (p. 3-6) (19:55)
- Ways to Represent a Function (p. 7-8) (7:49)
- Finding the Domain of a Function (p. 9) (4:31)
- Piecewise Functions (p. 10) (9:29)
- Even vs Odd vs Neither (p. 11-12) (6:02)
- Increasing, Decreasing, Constant (p. 13) (2:57)
- Essential Functions (p. 14-19) (15:15)
- Transforming Functions (p. 20-22) (12:22)
- Combinations of Functions (p. 23) (4:11)
- Composite Functions (p. 24) (6:26)
- Exponential Functions (p. 25) (5:01)
- Inverse Functions (p. 26-28) (11:28)
- Logarithms (p. 29-31) (9:58)
- Exponents and Logs - Side by Side (p. 32-36) (11:19)
- Linear Functions (p. 37-39) (10:20)
- Solving Inequalities (p. 40-41) (10:50)
- Rational Functions (p. 42-45) (16:34)

**Your Math Tutor: Marty**

Marty attended the University of Florida, where he earned a Bachelor of Science in statistics, a Bachelor of Arts in mathematics, and a Master of Science in electrical engineering.

While working as a teaching assistant for math and physics professors, he also did research on control systems. Later, he also taught high school physics and AP Computer Science.

Marty prides himself on making difficult concepts easier to understand. He’s been tutoring since he was a teenager, and he believes that anybody is capable of learning tough subjects with the right help.

Hit him up at [email protected].

**Other Courses We Cover at Auburn**

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