1. Derivatives

3hr

1.1.1. Basic Differentiation Rules7 min

1.1.2. Example: Derivative of a polynomial6 min

1.1.3. Derivatives of Exponential and Trigonometric Functions5 min

1.1.4. Example: Differentiating more complex functions7 min

1.1.5. Practice: Differentiating functions 13 min

1.1.6. Practice: Differentiating functions 22 min

1.2.1. Derivatives as Tangent Lines2 min

1.2.2. Derivatives as Instantaneous Rates of Change3 min

1.2.3. Example: Finding the tangent line8 min

1.2.4. Practice: Solving for the tangent line 14 min

1.2.5. Practice: Solving for the tangent line 2

1.3.1. The Product Rule49 sec

1.3.2. Example2 min

1.3.3. Example2 min

1.3.4. Practice2 min

1.4.1. The Chain Rule2 min

1.4.2. Example: Differentiating functions with the Chain Rule4 min

1.4.3. Example: Differentiating complicated functions8 min

1.5.1. The Quotient Rule1 min

1.5.2. Example2 min

1.5.3. Practice4 min

1.6.1. Derivatives of Trigonometric Functions1 min

1.7.1. Derivatives of Exponential Functions1 min

1.7.2. Example52 sec

1.7.3. Example3 min

1.7.4. Practice1 min

1.8.1. Derivatives of Logarithmic Functions1 min

1.8.2. Example56 sec

1.8.3. Example2 min

1.8.4. Practice2 min

1.8.5. Practice: Log and Ln2 min

1.9.1. Higher Order Derivatives2 min

1.9.2. Example3 min

1.9.3. Practice2 min

1.9.4. Practice2 min

1.10.1. Implicit Differentiation4 min

1.10.2. Example: Implicitly differentiating a function7 min

1.10.3. Logarithmic Differentiation2 min

1.10.4. Example: Using logarithmic differentiation7 min

1.10.5. Practice: Logarithmic differentiation4 min

1.11.1. Linear Approximation4 min

1.11.2. Example: Approximating a function by its tangent line5 min

1.11.3. Practice: Linear Approximation4 min

1.11.4. Practice: Relative Error6 min

1.12.1. L'Hopital's Rule4 min

1.12.2. Example: Computing a limit with L'Hopital's Rule4 min

1.12.3. Example: Computing a limit without L'Hopital's Rule2 min

1.12.4. Practice: L'Hopital's Rule6 min

1.13.1. Solving Physics Problems5 min

1.13.2. Example: Throwing a ball vertically6 min

1.13.3. Practice: Throwing a ball12 min

1.Q. Checkpoint Quiz5 Qns

2. Vector-Valued Functions

2.9hr

2.1.1. Vector Basics9 min

2.1.2. Vector Operations15 min

2.1.3. Example: Vector Operations13 min

2.1.4. Example: Linear Combinations7 min

2.1.5. Practice: Vector Operations

2.2.1. Functions in Several Variables2 min

2.2.2. Vector-Valued Functions8 min

2.2.3. Example: Domains of functions in one variable2 min

2.2.4. Example: Domains of vector-valued functions4 min

2.2.5. Practice: Domain of a function 12 min

2.2.6. Practice: Domain of a vector-valued function 25 min

2.3.1. Parametric Curves in 3D2 min

2.3.2. Graphing Planar Curves and Space Curves6 min

2.3.3. Eliminating Parameters3 min

2.3.4. Example: Sketching two-dimensional vector-valued functions7 min

2.3.5. Example: Eliminating a parameter6 min

2.3.6. Example: Parallel vectors8 min

2.3.7. Practice: Graphing a Vector-Valued Function15 min

2.3.8. Practice: Determining Vector-Valued Functions with conditions12 min

2.4.1. Inverse Functions7 min

2.4.2. Inverse Trigonometric Functions13 min

2.4.3. Example: Computing inverse trigonometric functions of numbers4 min

2.4.4. Example: Computing inverses of the same trigonometric function10 min

2.4.5. Example: Computing trigonometric functions of different inverse trigonometric functions.5 min

2.4.6. Practice: Inverse Trigonometric Functions 12 min

2.4.7. Practice: Inverse Trigonometric Functions 210 min

2.Q. Checkpoint Quiz: Vector-Valued Functions2 Qns

3. Derivatives of Vector Valued Functions

2hr

3.1.1. Derivatives of Vector-Valued Functions3 min

3.1.2. Displacement, Velocity and Acceleration6 min

3.1.3. Example: Computing derivatives of vector-valued functions2 min

3.1.4. Practice: Computing the Acceleration of a Particle2 min

3.2.1. Equations of Lines in

\mathbb{R}^3

6 min

3.2.2. Example: Equations of Lines in

\mathbb{R}^3

8 min

3.2.3. Practice: Equations of Lines in

\mathbb{R}^3

3.2.4. Equations of Planes in

\mathbb{R}^3

7 min

3.2.5. Example: Equations of Planes in

\mathbb{R}^3

5 min

3.2.6. Practice: Equations of Planes in

\mathbb{R}^3

3.2.7. Distance Between a Point and a Plane4 min

3.2.8. Example: Distance Between a Point and a Plane7 min

3.2.9. Practice: Distance Between a Point and a Plane

3.2.10. Distance Between a Point and a Line5 min

3.2.11. Example: Distance Between a Point and a Line8 min

3.2.12. Practice: Distance Between a Point and a Line

3.2.13. Closest Point on a Plane8 min

3.3.1. Norm of a Vector7 min

3.3.2. Example: Norm of a Vector6 min

3.3.3. Practice: Norm of a Vector

3.3.4. Dot Product5 min

3.3.5. Example: Dot product5 min

3.3.6. Properties of the Dot Product5 min

3.3.7. Example: Properties of the Dot Product8 min

3.3.8. Practice: Properties of the Dot Product

3.3.9. Projections6 min

3.3.10. Example: Projections6 min

3.3.11. Practice: Projections

3.3.12. Practice: Projections

3.3.13. Practice: Projections

3.Q. Checkpoint Quiz: Space Curves2 Qns

4. Applications of Differentiation

1.2hr

5. Integrals

1hr

6. Integration Techniques

47min

7. Applications of Integration

48min

8. Differential Equations

1.5hr

8.1.1. Differential Equations8 min

8.1.2. Direction Fields/Slope Fields5 min

8.1.3. Practice Question: DE Solution Graphs3 min

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

8.1.5. Practice

8.2.1. Separable First Order Differential Equations3 min

8.2.2. Practice (separable DE)2 min

8.2.3. Practice (IVP)3 min

8.2.4. Practice (IVP)3 min

8.2.5. Practice (IVP*)5 min

8.2.6. Practice (separable DE)1 min

8.3.1. Linear First Order Differential Equations7 min

8.3.2. Practice (integrating factor)1 min

8.3.3. Practice (linear DE)3 min

8.3.4. Practice (IVP)3 min

8.3.5. Practice (IVP)4 min

8.4.1. Common DE Applications (Word Problems)

8.4.2. Practice (population)3 min

8.4.3. Practice (population)4 min

8.4.4. Practice (cooling & heating)3 min

8.4.5. Practice (mixing tank)6 min

8.4.6. Practice (mixing tank)8 min

8.5.1. Second-Order Reducible DE

8.5.2. Practice: Dependent Variable Missing

8.5.3. Practice: Independent Variable Missing

8.6.1. Theory: Harmonic Motion6 min

8.6.2. Concept Clarifier: Harmonic Motion5 min

8.7.1. Problems: Differential Equations3 Qns

8.Q. DE Quiz4 Qns

9. Complex Numbers

1.4hr

9.I. Chapter Overview1 min

9.1.1. Basics of Complex Numbers10 min

9.1.2. Operations With Complex Numbers16 min

9.1.3. Example: Operations With Complex Numbers10 min

9.1.4. Practice: Operations With Complex Numbers

9.2.1. Polar Form of Complex Numbers10 min

9.2.2. Example: Polar Form of Complex Numbers12 min

9.2.3. Practice: Polar Form of Complex Numbers

9.2.4. Practice: Polar Form of Complex Numbers

9.3.1. Powers of Complex Numbers3 min

9.3.2. Example: Powers of Complex Numbers6 min

9.3.3. Roots of Complex Numbers9 min

9.3.4. Example: Roots of Complex Numbers9 min

9.3.5. Practice: Powers and Roots of Complex Numbers

9.Q. Complex Numbers Checkpoint Quiz6 Qns

Mock Exams

ME.1. Test 1 - Mock Assessment 19 Qns

ME.2. Test 2 - Mock Assessment10 Qns

ME.3. Final Exam - Mock Assessment39 Qns

APSC 171

Course Overview

Grade Boosters

1. Derivatives

2. Vector-Valued Functions

3. Derivatives of Vector Valued Functions

4. Applications of Differentiation

5. Integrals

6. Integration Techniques

7. Applications of Integration

8. Differential Equations

9. Complex Numbers

Mock Exams

Test 2 Overview

Available Test 2 Grade Boosters

Test 2 Mock

Included with Wizeprep Plus

Course Notes