Calculus 2

University Study Guides

Course Overview

Lessons & Practice

I. Welcome

1. Review: 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. 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

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. Applications of Integrals

1.6hr

3.1.1. Average value of a function3 min

3.1.2. Example2 min

3.1.3. Practice2 min

3.1.4. Displacement, Velocity, and Acceleration4 min

3.1.5. Rates of Change and Integrals3 min

3.2.1. Area between Curves3 min

3.2.2. Practice4 min

3.2.3. Practice3 min

3.2.4. Practice (multiple regions)4 min

3.3.1. Volumes - Cross Sections Method3 min

3.3.2. Practice4 min

3.3.3. Practice3 min

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

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

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

3.4.4. Practice (around a line)3 min

3.5.1. Volumes of Revolution (Cylindrical Shells)4 min

3.5.2. Practice2 min

3.6.1. Arc Length of a Curve3 min

3.6.2. Practice6 min

3.6.3. Practice4 min

3.7.1. Surface Area of Revolution1 min

3.7.2. Example5 min

3.7.3. Practice

3.8.1. Distribution Functions4 min

3.8.2. Practice: PDF3 min

3.8.3. Practice: CDF2 min

3.8.4. Mean, Median, and Variance3 min

3.8.5. Practice2 min

3.8.6. Practice: Median1 min

3.9.1. Work2 min

3.9.2. Example3 min

3.9.3. Practice

3.Q. Applications of Integration Quiz7 Qns

4. Integration Techniques

2.6hr

4.1.1. Integration by Parts6 min

4.1.2. Practice4 min

4.1.3. Practice (w/

\ln

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

4.2.1. Trigonometric Integrals3 min

4.2.2. Practice (odd power of

\cos x

4.2.3. Practice (odd power of

\sin x

4.2.4. Practice (even powers of

\sin x

\cos x

4.2.5. Practice (even power of

\sec x

4.2.6. Practice (w/

\sec x \tan x

4.2.7. Practice (

\sin (mx)

\sin(nx)

4.2.8. Practice (special case

\sec x

4.2.9. Practice (special case

\sec^3x

4.2.10. Reduction Formula2 min

4.2.11. Practice5 min

4.2.12. Practice3 min

4.3.1. Trigonometric Substitution10 min

4.3.2. Practice6 min

4.3.3. Practice5 min

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

4.4.1. Partial Fractions Decomposition7 min

4.4.2. Practice (linear factors only)4 min

4.4.3. Practice (w/ quadratic factors)7 min

4.4.4. Practice (w/ long division)6 min

4.5.1. Strategies for Integration3 min

4.5.2. Practice (rationalizing substitution)4 min

4.5.3. Practice: Mixed Integrals4 min

4.5.4. Practic6 min

4.5.5. Practice5 min

4.5.6. Practice7 min

4.5.7. Practice7 min

4.6.1. The Midpoint Rule1 min

4.6.2. Example2 min

4.6.3. The Trapezoid Rule 1 min

4.6.4. Example2 min

4.6.5. Practice

4.6.6. Simpson's Rule1 min

4.6.7. Example2 min

4.6.8. Practice

4.6.9. Error Bounds for Approximations2 min

4.6.10. Practice

4.6.11. Numerical Integration (Summary)

4.Q. Integration Techniques Quiz18 Qns

5. Improper Integrals

40min

5.1.1. L'Hospital's Rule5 min

5.1.2. Practice2 min

5.1.3. Practice4 min

5.1.4. Practice4 min

5.2.1. Improper Integrals4 min

5.2.2. Practice (type 1)2 min

5.2.3. Practice (type 1)5 min

5.2.4. Practice (Type 2)5 min

5.3.1. Comparison Theorem for Improper Integrals3 min

5.3.2. Practice (type 1 - converges)3 min

5.3.3. Practice (type 2 - converges)4 min

5.3.4. Practice (type 2 - diverges)

5.Q. Improper Integral Quiz4 Qns

6. Sequences and Series

2hr

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

6.2.2. Practice2 min

6.2.3. Practice1 min

6.2.4. Practice3 min

6.2.5. Practice3 min

6.3.1. Integral Test1 min

6.3.2. Practice: Integral Test6 min

6.3.3. Practice: Integral Test5 min

6.4.1. Series and Limit Comparison Tests5 min

6.4.2. Practice (limit comparison test)2 min

6.4.3. Practice (limit comparison test)3 min

6.4.4. Practice (telescoping series*)6 min

6.4.5. Practice (series comparison test)5 min

6.4.6. Practice (series comparison test)2 min

6.4.7. Practice (telescoping series*)3 min

6.5.1. Absolute Convergence Test3 min

6.5.2. Practice5 min

6.5.3. Alternating Series Test2 min

6.5.4. Practice: AST5 min

6.6.1. Ratio Test2 min

6.6.2. Practice5 min

6.6.3. Practice2 min

6.6.4. Practice (recursive series*)4 min

6.7.1. Root Test1 min

6.7.2. Practice3 min

6.7.3. Practice: Root Test4 min

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

6.Q. Sequences and Series Quiz13 Qns

7. Power Series

1.4hr

7.1.1. Definitions of Power Series9 min

7.1.2. Practice (radius of convergence)2 min

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

7.1.4. Practice: Radius & Interval of Convergence4 min

7.2.1. Representing Functions as Power Series2 min

7.2.2. Practice2 min

7.2.3. Practice2 min

7.2.4. Practice (w/ partial fractions)7 min

7.2.5. Differentiation and Integration of Power Series3 min

7.2.6. Practice (differentiating power series)4 min

7.2.7. Practice (integrating power series)4 min

7.2.8. Practice (integrating power series*)8 min

7.3.1. Taylor and Maclaurin Series6 min

7.3.2. Practice (Taylor series)7 min

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

7.3.4. Practice (Maclaurin series)2 min

7.3.5. Practice (Maclaurin series)3 min

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

7.3.7. Practice (evaluating a series*)3 min

7.Q. Power Series Quiz10 Qns

8. Parametric & Polar Curves

1.8hr

8.1.1. Parametric Curves6 min

8.1.2. Practice (Cartesian equations)2 min

8.1.3. Practice (graphs)4 min

8.1.4. Practice (graphs)3 min

8.2.1. Tangents/Derivatives of Parametric Curves2 min

8.2.2. Practice (derivatives)2 min

8.2.3. Practice (horizontal/vertical tangents)5 min

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

8.2.5. Arc Length, Area, and Surface Area2 min

8.2.6. Practice (arc length)3 min

8.2.7. Practice (area)3 min

8.2.8. Practice (surface area)6 min

8.2.9. Practice (surface area)5 min

8.3.1. Polar Coordinates7 min

8.3.2. Graphing Polar Curves6 min

8.3.3. Practice (graphs)6 min

8.3.4. Practice (polar coordinates)2 min

8.3.5. Practice (matching graphs)4 min

8.4.1. Tangents/Derivatives of Polar Curves2 min

8.4.2. Practice (derivative)4 min

8.4.3. Practice (horizontal/vertical tangents)7 min

8.4.4. Arc Length, Area Under & Between Curves2 min

8.4.5. Practice (arc length)3 min

8.4.6. Practice (area inside curve)2 min

8.4.7. Practice (area inside curve)4 min

8.4.8. Practice (area between curves)8 min

8.Q. Parametric and polar curves Quiz6 Qns

9. Differential Equations

1.3hr

9.1.1. Differential Equations8 min

9.1.2. Direction Fields/Slope Fields5 min

9.1.3. Practice Question: DE Solution Graphs3 min

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

9.1.5. Practice

9.2.1. Separable First Order Differential Equations3 min

9.2.2. Practice (separable DE)2 min

9.2.3. Practice (IVP)3 min

9.2.4. Practice (IVP)3 min

9.2.5. Practice (IVP*)5 min

9.2.6. Practice (separable DE)1 min

9.3.1. Linear First Order Differential Equations7 min

9.3.2. Practice (integrating factor)1 min

9.3.3. Practice (linear DE)3 min

9.3.4. Practice (IVP)3 min

9.3.5. Practice (IVP)4 min

9.4.1. Common DE Applications (Word Problems)

9.4.2. Practice (population)3 min

9.4.3. Practice (population)4 min

9.4.4. Practice (cooling & heating)3 min

9.4.5. Practice (mixing tank)6 min

9.4.6. Practice (mixing tank)8 min

9.5.1. Second-Order Reducible DE

9.5.2. Practice: Dependent Variable Missing

9.5.3. Practice: Independent Variable Missing

9.Q. DE Quiz4 Qns

10. Vector Functions

55min

10.1.1. 3D Cooridnate System4 min

10.1.2. Vectors7 min

10.1.3. Dot Product7 min

10.1.4. Cross Product6 min

10.1.5. Equations of Lines & Planes10 min

10.1.6. Cylinder & Quadric Surface

10.1.7. Example: Quadratic Surfaces (1)3 min

10.1.8. Example: Quadratic Surfaces (2)2 min

10.1.9. Cylindrical & Spherical Coordinates

10.2.1. Vector-Valued Functions5 min

10.2.2. Arc Length6 min

10.2.3. Curvature5 min

11. Multivariable Functions

1.1hr

11.1.1. Functions of Several Variables5 min

11.1.2. Practice3 min

11.2.1. Partial derivatives6 min

11.2.2. Practice: First Partial derivatives2 min

11.2.3. Practice: Second Partial Derivatives3 min

11.3.1. Chain Rule7 min

11.3.2. Practice: Chain Rule2 min

11.3.3. Practice: Chain Rule2 min

11.3.4. Practice: Chain Rule*3 min

11.3.5. Implicit Differentiation2 min

11.4.1. Gradient and directional derivative7 min

11.4.2. Practice: Gradient and directional derivative

11.5.1. Tangent plane3 min

11.5.2. Practice: Tangent Plane

11.5.3. Linear (Tangent Plane) Approximation3 min

11.5.4. Practice: Linear approximation

11.6.1. Differentials4 min

11.6.2. Practice: Differentials

11.6.3. Practice: Differentials

11.8.1. Local Max & Min4 min

11.8.2. Absolute Max & Min5 min

11.8.3. Lagrange Multipliers3 min

11.8.4. Practice: Lagrange Multipliers

11.8.5. Practice: Lagrange Multipliers

11.9.1. Multivariable Functions Quiz12 Qns

12. Bonus: Integral calculus in several variables (Videos Coming Soon)

3min

12.1.1. Double Integration (rectangular)

12.1.2. Practice: Double integration

12.1.3. Practice: Changing the order of integration

12.1.4. Practice: Changing the order of integration

12.1.5. Interpretation of a Double Integral

12.1.6. Practice: Volume under a surface

12.2.1. Double Integration (polar)

12.2.2. Practice: Double integration (polar)

12.3.1. Triple Integration (rectangular)

12.3.2. Practice: Triple integration (rectangular)

12.3.3. Practice: Triple integration (rectangular)

12.4.1. Cylindrical coordinates

12.4.2. Triple Integration (cylindrical)

12.4.3. Practice: Cylindrical coordinates

12.4.4. Example: Triple integration (cylindrical)

12.4.5. Practice: Triple integration (cylindrical)

12.5.1. Spherical coordinates

12.5.2. Triple Integration (spherical)

12.5.3. Practice: Triple integration (spherical)

12.5.4. Practice: Triple integration (spherical)

12.5.5. Practice: Triple integration (spherical)3 min

12.6.1. Improper Integrals

12.6.2. Practice: Improper integrals

12.6.3. Practice: Improper integrals

12.7.1. Moments and centre of mass

12.7.2. Practice: Centroid

12.7.3. Moment of inertia

12.7.4. Practice: Moment of inertia

12.8.1. Multiple Integrals Quiz15 Qns

12.8.2. Centroid, centre of mass, moment of inertia Quiz8 Qns

13. Vector Calculus [Coming Soon!]

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Answered

A

Alex2004

Do you have any midterm exam/solutions from the past for this course?

J

Jarrett N

Instructor

Hello!

This Calc 2 study template is a generic template for many Calc 2 courses from multiple universities. Therefore, we do not have midterm exam/solutions for one specific university. However, many of our live prep sessions that we offer for many universities are course-specific depending on your university and course code. We offer many similar past-exam questions! You can also find midterm exams/solutions through your university library sometimes, or other external resources. 

I hope this helps!

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