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Calculus 2
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Important Note About the Order of Topics
Integration Techniques Part 1 - Substitution & IBP — Topic Review (⏱️ <51 min)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Substitution Practice Exam Solutions (2:55)
Integration by Parts Practice Exam Solutions (24:42)
Integration by Parts and Substitution Practice Exam Solutions (15:14)
Integration Techniques Part 2 - Trig Integrals & Trig Sub — Topic Review (⏱️ <80 min)
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
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)
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
Practice Exam Questions
Practice Exam Questions Answer Key
PFD Practice Exam Solutions (16:46)
Rationalizing Substitution Practice Exam Solutions (9:36)
Which Method Should I Use? Practice Exam Solutions (47:09)
Improper Integrals, Approximation Methods, & Function Growth Rates — Topic Review (⏱️ <52 min)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Evaluating Limits Using Growth Rates Practice Exam Solutions (2:59)
Improper Integrals Practice Exam Solutions (16:48)
Integration Applications Part 1 - Area Between Curves and Volumes — Topic Review (⏱️ <72 min)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Areas Between Curves Practice Exam Solutions (14:41)
Volume by Cross Sectional Area Practice Exam Solutions (11:16)
Disk/Washer Method Practice Exam Solutions (36:25)
Shell Method Practice Exam Solutions (35:35)
Integration Applications Part 2 - Work and Average Value — Topic Review (⏱️ <63 min)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Work Involving Springs Practice Exam Solutions (11:16)
Work Involving Lifting Objects Practice Exam Solutions (23:02)
Work Involving Pumping Fluids Practice Exam Solutions (16:56)
Average Value of a Function Practice Exam Solutions (4:58)
Integration Applications Part 3 - Arc Length, Surface Area, Physics, and Probability — Topic Review (⏱️ < 74 min)
Study Guide (fill this in as you watch the videos!)
Arc Length (p. 3-5) (11:32)
Area of Surfaces of Revolution (p. 6-7) (9:21)
Hydrostatic Pressure and Force (p. 8-10) (15:59)
Center of Mass (p. 11-15) (19:10)
Probability (p. 16-19) (17:42)
Integration Applications Part 3 - Arc Length, Surface Area, Physics, and Probability — Practice Exam Questions
Practice Exam Questions
Practice Exam Questions Answer Key
Arc Length Practice Exam Solutions (17:38)
Surface Area Practice Exam Solutions (10:49)
Hydrostatic Force and Pressure Practice Exam Solutions (20:41)
Center of Mass Practice Exam Solutions (19:46)
Probability Practice Exam Solutions (7:33)
Sequences — Topic Review (⏱️ <40 min)
Study Guide (fill this in as you watch the videos!)
Sequences - Overview (p. 3-6) (16:16)
Monotonic and Bounded Sequences (p. 7-8) (9:13)
Recursive Sequences (p. 9) (4:56)
Sequence Convergence Theorems (p. 10-12) (8:41)
Sequences — Practice Exam Questions
Practice Exam Questions
Practice Exam Questions Answer Key
Sequences Practice Exam Solutions (13:23)
Series Overview, Geometric Series, Telescoping Series, Integral Test, and p-Series — Topic Review (⏱️< 46 min)
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
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)
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
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)
Study Guide (fill this in as you watch the videos!)
Ratio Test (p. 3-5) (13:34)
Root Test (p. 6-7) (4:37)
General Strategies for Picking the Right Test (p. 8-10) (7:43)
The Ratio and Root Tests — Practice Exam Questions
Practice Exam Questions
Practice Exam Questions Answer Key
Ratio Test Practice Exam Solutions (6:09)
Root Test Practice Exam Solutions (3:29)
Mixed Practice Practice Exam Solutions (16:55)
Power Series — Topic Review (⏱️ <49 min)
Study Guide (fill this in as you watch the videos!)
Power Series - Overview (p. 3-5) (14:06)
Representing Functions as Power Series (p. 6-7) (7:58)
Differentiating & Integrating Power Series (p.8-10) (17:13)
Approximation Using Power Series (p. 11-12) (9:28)
Power Series — Practice Exam Questions
Practice Exam Questions
Practice Exam Questions Answer Key
Radius and Interval of Convergence Practice Exam Solutions (9:12)
Representing Functions as Power Series Practice Exam Solutions (18:46)
Taylor & Maclaurin Series — Topic Review (⏱️ <44 min)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Finding Taylor Series Practice Exam Solutions (19:49)
Taylor's Inequality Practice Exam Solutions (11:10)
Finding Sums & Derivatives Using Known Taylor Series (8:58)
Parametric Equations — Topic Review (⏱️ <40 min)
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
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)
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
Practice Exam Questions
Practice Exam Questions Answer Key
Converting Between Polar and Rectangular Coordinates Practice Exam Solutions (4:36)
Areas Involving Polar Curves Practice Exam Solutions (43:01)
Derivatives Involving Polar Curves Practice Exam Solutions (3:56)
Intro to Differential Equations — Topic Review
Coming Soon!
Intro to Differential Equations — Practice Exam Questions
Coming Soon!
Vectors — Topic Review
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
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
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
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
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)
Trig Integrals with Sine and Cosine with Different Angles (p. 8)
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