1. Review of Derivatives

1.3hr

1.1.1. Interpretation of Derivatives8 min

1.1.2. Practice: Definition of Derivative6 min

1.1.3. Practice: Differentiability4 min

1.2.1. Derivative Rules7 min

1.2.2. Example: Derivative Rules4 min

1.2.3. Product, Quotient, and Chain Rule4 min

1.2.4. Example: Product, Quotient, and Chain Rule8 min

1.2.5. Practice: Finding a Derivative4 min

1.2.6. Practice: Finding a Derivative4 min

1.2.7. Practice: Higher Order Derivative6 min

1.2.8. Practice: Product Rule*6 min

1.2.9. Practice: Chain Rule*6 min

1.3.1. Tangent and Normal Lines4 min

1.3.2. Practice: Equation of Tangent Line

1.3.3. Practice: Slope of a Normal Line3 min

1.4.1. Implicit Differentiation1 min

1.4.2. Practice: Implicit differentiation4 min

2. Review of Integration

1.5hr

2.I. What is Integration?

2.1.1. Antiderivatives & Indefinite Integrals6 min

2.1.2. Practice1 min

2.1.3. Practice1 min

2.1.4. Practice (initial condition)2 min

2.2.1. Review: Sigma Notation6 min

2.2.2. Practice (index

i\neq1

)3 min

2.2.3. Practice (w/ limits)3 min

2.2.4. Practice (telescoping sum)2 min

2.2.5. Riemann Sums7 min

2.2.6. Practice (left/right sums)2 min

2.2.7. Practice (area)3 min

2.2.8. Practice (area) *Tricky3 min

2.3.1. Definite Integrals 3 min

2.3.2. Practice1 min

2.3.3. Practice *Tricky3 min

2.3.4. Properties of Definite Integrals5 min

2.3.5. Practice1 min

2.4.1. Fundamental Theorem of Calculus 13 min

2.4.2. Practice2 min

2.4.3. Practice (w/ limit)2 min

2.4.4. Fundamental Theorem of Calculus 23 min

2.4.5. Practice2 min

2.4.6. Practice1 min

2.4.7. Practice (absolute values)3 min

2.5.1. U-Substitution (Integration by Substitution)6 min

2.5.2. Practice2 min

2.5.3. Practice3 min

2.5.4. Practice (definite integral)3 min

2.5.5. Practice (w/ back-sub)4 min

2.5.6. Short-Cut for U-Substitution3 min

2.Q. Integration Quiz18 Qns

3. Techniques of Integration

3hr

3.1.1. Integration by Parts6 min

3.1.2. Practice4 min

3.1.3. Practice (w/

\ln

)2 min

3.1.4. Practice (w/ exp & trig)6 min

3.2.1. Partial Fractions Decomposition7 min

3.2.2. Practice (linear factors only)4 min

3.2.3. Practice (w/ quadratic factors)7 min

3.2.4. Practice (w/ long division)6 min

3.3.1. Trigonometric Integrals3 min

3.3.2. Practice (odd power of

\cos x

)3 min

3.3.3. Practice (odd power of

\sin x

)3 min

3.3.4. Practice (even powers of

\sin x

&

\cos x

)2 min

3.3.5. Practice (even power of

\sec x

)4 min

3.3.6. Practice (w/

\sec x \tan x

)3 min

3.3.7. Practice (

\sin (mx)

&

\sin(nx)

)1 min

3.3.8. Practice (special case

\sec x

)3 min

3.3.9. Practice (special case

\sec^3x

)5 min

3.3.10. Reduction Formula2 min

3.3.11. Practice5 min

3.3.12. Practice3 min

3.4.1. Trigonometric Substitution10 min

3.4.2. Practice6 min

3.4.3. Practice5 min

3.4.4. Practice (w/ completing the square)6 min

3.5.1. Improper Integrals4 min

3.5.2. Practice (type 1)2 min

3.5.3. Practice (type 1)5 min

3.5.4. Practice (Type 2)5 min

3.6.1. L'Hospital's Rule5 min

3.6.2. Practice2 min

3.6.3. Practice4 min

3.6.4. Practice4 min

3.7.1. Comparison Theorem for Improper Integrals3 min

3.7.2. Practice (type 1 - converges)3 min

3.7.3. Practice (type 2 - converges)4 min

3.7.4. Practice (type 2 - diverges)

3.8.1. Strategies for Integration3 min

3.8.2. Practice (rationalizing substitution)4 min

3.8.3. Practice: Mixed Integrals4 min

3.Q. Integration Techniques Quiz18 Qns

4. Applications of Integration

2.2hr

4.1.1. Average value of a function3 min

4.1.2. Example2 min

4.1.3. Practice2 min

4.1.4. Displacement, Velocity, and Acceleration4 min

4.1.5. Rates of Change and Integrals3 min

4.2.1. Area between Curves3 min

4.2.2. Practice4 min

4.2.3. Practice3 min

4.2.4. Practice (multiple regions)4 min

4.3.1. Volumes - Cross Sections Method3 min

4.3.2. Practice4 min

4.3.3. Practice3 min

4.4.1. Volumes of Revolution (Disk/Washer)3 min

4.4.2. Practice (around the x-axis)2 min

4.4.3. Practice (around the y-axis)3 min

4.4.4. Practice (around a line)3 min

4.5.1. Volumes of Revolution (Cylindrical Shells)4 min

4.5.2. Practice2 min

4.6.1. Arc Length of a Curve3 min

4.6.2. Practice6 min

4.6.3. Practice4 min

4.7.1. Surface Area of Revolution1 min

4.9.1. Differential Equations8 min

4.9.2. Direction Fields/Slope Fields5 min

4.9.3. Practice Question: DE Solution Graphs3 min

4.9.4. Euler's Method (Approximating Solutions)4 min

4.9.5. Practice

4.10.1. Separable First Order Differential Equations3 min

4.10.2. Practice (separable DE)2 min

4.10.3. Practice (IVP)3 min

4.10.4. Practice (IVP)3 min

4.10.5. Practice (IVP*)5 min

4.10.6. Practice (separable DE)1 min

4.11.1. Linear (First Order) Differential Equations7 min

4.11.2. Practice (integrating factor)1 min

4.11.3. Practice (linear DE)3 min

4.11.4. Practice (IVP)3 min

4.11.5. Practice (IVP)4 min

4.Q. Applications of Integration Quiz7 Qns

5. Parametric Curves and Polar Curves

1.8hr

5.1.1. Parametric Curves6 min

5.1.2. Practice (Cartesian equations)2 min

5.1.3. Practice (graphs)4 min

5.1.4. Practice (graphs)3 min

5.2.1. Tangents/Derivatives of Parametric Curves2 min

5.2.2. Practice (derivatives)2 min

5.2.3. Practice (horizontal/vertical tangents)5 min

5.2.4. Practice (horizontal/vertical tangents*)6 min

5.2.5. Arc Length, Area, and Surface Area2 min

5.2.6. Practice (arc length)3 min

5.2.7. Practice (area)3 min

5.2.8. Practice (surface area)6 min

5.2.9. Practice (surface area)5 min

5.3.1. Polar Coordinates7 min

5.3.2. Graphing Polar Curves6 min

5.3.3. Practice (graphs)6 min

5.3.4. Practice (polar coordinates)2 min

5.3.5. Practice (matching graphs)4 min

5.4.1. Tangents/Derivatives of Polar Curves2 min

5.4.2. Practice (derivative)4 min

5.4.3. Practice (horizontal/vertical tangents)7 min

5.4.4. Arc Length, Area Under & Between Curves2 min

5.4.5. Practice (arc length)3 min

5.4.6. Practice (area inside curve)2 min

5.4.7. Practice (area inside curve)4 min

5.4.8. Practice (area between curves)8 min

5.Q. Parametric and polar curves Quiz6 Qns

6. Sequences, Series, and Power Series

3hr

6.1.1. Sequences8 min

6.1.2. Series7 min

6.1.3. Practice (Partial sums)2 min

6.1.4. Practice (Geometric series)2 min

6.1.5. Practice (Geometric series)3 min

6.1.6. Practice: Series Application6 min

6.1.7. How to Test if a Series Converges?

6.2.1. Integral Test1 min

6.2.2. Practice: Integral Test6 min

6.2.3. Practice: Integral Test5 min

6.2.4. Series and Limit Comparison Tests5 min

6.2.5. Practice (limit comparison test)2 min

6.2.6. Practice (limit comparison test)3 min

6.2.7. Practice (telescoping series*)6 min

6.2.8. Practice (series comparison test)5 min

6.2.9. Practice (series comparison test)2 min

6.2.10. Practice (telescoping series*)3 min

6.2.11. Ratio Test2 min

6.2.12. Practice (Ratio Test)5 min

6.2.13. Practice (Ratio Test)2 min

6.2.14. Practice (recursive series*)4 min

6.2.15. Root Test1 min

6.2.16. Practice (Root Test)3 min

6.2.17. Practice (Root Test)4 min

6.2.18. How to Pick Which Convergence Test to Use?6 min

6.3.1. Absolute Convergence Test3 min

6.3.2. Practice5 min

6.3.3. Alternating Series Test2 min

6.3.4. Practice: AST5 min

6.4.1. Definitions of Power Series9 min

6.4.2. Practice (radius of convergence)2 min

6.4.3. Practice (radius & interval of convergence)7 min

6.4.4. Practice: Radius & Interval of Convergence4 min

6.4.5. Representing Functions as Power Series2 min

6.4.6. Practice2 min

6.4.7. Practice2 min

6.4.8. Practice (w/ partial fractions)7 min

6.4.9. Differentiation and Integration of Power Series3 min

6.4.10. Practice (differentiating power series)4 min

6.4.11. Practice (integrating power series)4 min

6.4.12. Practice (integrating power series*)8 min

6.5.1. Taylor and Maclaurin Series6 min

6.5.2. Practice (Taylor series)7 min

6.5.3. Common Maclaurin Series (Memorize!)*5 min

6.5.4. Practice (Maclaurin series)2 min

6.5.5. Practice (Maclaurin series)3 min

6.5.6. Practice (Maclaurin series of an integral)2 min

6.5.7. Practice (evaluating a series*)3 min

6.6.1. Test of Divergence (nth Term Limit Test)2 min

6.Q. Sequences and Series Quiz13 Qns

7. Vectors and Coordinate Geometry in 3-Space

34min

7.1.1. 3D Cooridnate System4 min

7.1.2. Vectors in 3-Space7 min

7.2.1. Dot Product in 3-Space7 min

7.2.2. Cross Product in 3-Space6 min

7.3.1. Equations of Planes and Lines10 min

8. Functions of Several Variables

8min

8.1.1. Functions of Several Variables5 min

8.1.2. Practice3 min

8.2.1. Multivariable Functions Quiz12 Qns

9. Applications of Partial Derivatives

29min

9.I. Extreme Values

9.1.1. Classifying Critical Points5 min

9.1.2. Example (Classifying Critical Points)5 min

9.1.3. Practice (Classifying Critical Points)4 min

9.1.4. Practice (Classifying Critical Points)4 min

9.2.1. Lagrange Multipliers3 min

9.2.2. Practice (Lagrange Multipliers)3 min

9.2.3. Practice (Lagrange Multipliers)4 min

9.3.1. Newton's Method1 min

NMM 1414A/B

Course Overview

1. Review of Derivatives

2. Review of Integration

3. Techniques of Integration

4. Applications of Integration

5. Parametric Curves and Polar Curves

6. Sequences, Series, and Power Series

7. Vectors and Coordinate Geometry in 3-Space

8. Functions of Several Variables

9. Applications of Partial Derivatives

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