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Integration Techniques Part 1 - Substitution & IBP — Topic Review (⏱️ <51 min)
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- 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)
Integration Techniques Part 1 - Substitution & IBP — Practice Exam Questions
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Integration Techniques Part 2 - Trig Integrals & Trig Sub — Topic Review (⏱️ <80 min)
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- 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)
Integration Techniques Part 2 - Trig Integrals & Trig Sub — Practice Exam Questions
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- 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)
Integration Techniques Part 3 - PFD & Rationalizing Substitution — Topic Review (⏱️ <56 min)
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- 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)
Integration Techniques Part 3 - PFD & Rationalizing Substitution — Practice Exam Questions
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Improper Integrals, Approximation Methods, & Function Growth Rates — Topic Review (⏱️ <52 min)
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- 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)
Improper Integrals, Approximation Methods, & Function Growth Rates — Practice Exam Questions
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Integration Applications Part 1 - Area Between Curves and Volumes — Topic Review (⏱️ <72 min)
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- 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)
Integration Applications Part 1 - Area Between Curves and Volumes — Practice Exam Questions
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Integration Applications Part 2 - Work and Average Value — Topic Review (⏱️ <63 min)
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- 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)
Integration Applications Part 2 - Work, Force, and Average Value — Practice Exam Questions
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Integration Applications Part 3 - Arc Length, Surface Area, Physics, and Probability — Topic Review (⏱️ < 74 min)
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Integration Applications Part 3 - Arc Length, Surface Area, Physics, and Probability — Practice Exam Questions
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Sequences — Topic Review (⏱️ <40 min)
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Sequences — Practice Exam Questions
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Series Overview, Geometric Series, Telescoping Series, Integral Test, and p-Series — Topic Review (⏱️< 46 min)
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- 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)
Series Overview, Geometric Series, Telescoping Series, Integral Test, and p-Series — Practice Exam Questions
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- 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)
Comparison Tests, Alternating Series, and Absolute & Conditional Convergence — Topic Review (⏱️ <57 min)
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- 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)
Comparison Tests, Alternating Series, and Absolute & Conditional Convergence — Practice Exam Questions
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- 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)
The Ratio and Root Tests — Topic Review (⏱️ <26 min)
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The Ratio and Root Tests — Practice Exam Questions
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Power Series — Topic Review (⏱️ <49 min)
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Power Series — Practice Exam Questions
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Taylor & Maclaurin Series — Topic Review (⏱️ <44 min)
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- 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)
Taylor & Maclaurin Series — Practice Exam Questions
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Parametric Equations — Topic Review (⏱️ <40 min)
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- 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)
Parametric Equations — Practice Exam Questions
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- 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)
Polar Coordinates — Topic Review (⏱️ <77 min)
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- 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)
Polar Coordinates — Practice Exam Questions
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Intro to Differential Equations — Topic Review
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Intro to Differential Equations — Practice Exam Questions
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Vectors — Topic Review
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- 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)
Vectors — Practice Exam Questions
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- 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)
[OPTIONAL] Sh*t You Forgot from Calc 1
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- 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)
[OPTIONAL] Sh*t You Forgot from Trig
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- 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)
[OPTIONAL] Sh*t You Forgot from Precalc
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- 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.
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