1. Functions

4hr

1.1.1. Basic Graphs6 min

1.1.2. Example2 min

1.1.3. Practice (Level 1)2 min

1.1.4. Practice (Level 2)1 min

1.1.5. Practice (Level 2)2 min

1.1.6. Practice (Level 3)2 min

1.1.7. Reference Sheet: Basic Graphs

1.2.1. Functions7 min

1.2.2. Domain and Range of a Function5 min

1.2.3. Example4 min

1.2.4. Practice (Level 1)56 sec

1.2.5. Practice (Level 2)44 sec

1.2.6. Practice (Level 3)2 min

1.3.1. Function Notation6 min

1.3.2. Example6 min

1.3.3. Practice (Level 1)2 min

1.3.4. Practice (Level 2)1 min

1.3.5. Practice (Level 3)3 min

1.4.1. Linear Equations4 min

1.4.2. Practice Level 113 min

1.4.3. Practice Level 27 min

1.4.4. Parallel & Perpendicular Lines7 min

1.4.5. Practice Level 35 min

1.5.1. Graphing Linear Equations - Table of Values3 min

1.5.2. Graphing Linear Equations - Slope y-Intercept Form5 min

1.5.3. Graphing Linear Equations - Using Intercepts4 min

1.5.4. Practice4 min

1.6.1. Linear Regression8 min

1.6.2. Example: Linear Regression4 min

1.6.3. Linear Regression

1.6.4. Practice: Linear Regression4 min

1.7.1. Domain2 min

1.7.2. Range2 min

1.7.3. Example2 min

1.7.4. Practice 40 sec

1.7.5. Practice 3 min

1.8.1. Activity: Exploring Quadratic Relations

1.8.2. Quadratic Functions3 min

1.8.3. Example7 min

1.8.4. Practice Level 15 min

1.8.5. Practice Level 25 min

1.8.6. Practice Level 2

1.8.7. Practice Level 37 min

1.9.1. Rational Functions4 min

1.9.2. Solving Rational Equations3 min

1.10.1. Radical Functions59 sec

1.10.2. Solving Radical Equations5 min

1.10.3. Example5 min

1.10.4. Practice8 min

1.11.1. Exponential Functions3 min

1.11.2. Example1 min

1.11.3. Example2 min

1.12.1. Applications of Exponential Functions1 min

1.12.2. Example2 min

1.12.3. Practice Level 14 min

1.12.4. Practice Level 25 min

1.12.5. Practice Level 33 min

1.13.1. Logarithmic Functions4 min

1.13.2. Example3 min

1.13.3. Example:3 min

1.13.4. Practice2 min

1.14.1. Applications of Logarithmic Functions30 sec

1.14.2. Example

1.14.3. Practice Level 1

1.14.4. Practice Level 2

1.14.5. Practice Level 3

2. Linear Algebra (Systems of Linear Equations)

2.3hr

2.1.1. Intro to Systems of Linear Equations (Simultaneous Equations)3 min

2.2.1. Solving by Substitution12 min

2.2.2. Example5 min

2.2.3. Practice Level 12 min

2.2.4. Practice Level 25 min

2.2.5. Practice Level 37 min

2.3.1. Solving by Simple Elimination12 min

2.3.2. Example3 min

2.3.3. Practice Level 13 min

2.3.4. Practice Level 22 min

2.3.5. Practice Level 24 min

2.4.1. Solving by Multiplication before Elimination8 min

2.4.2. Example4 min

2.4.3. Example4 min

2.4.4. Practice Level 14 min

2.4.5. Practice Level 24 min

2.4.6. Practice5 min

2.5.1. No Solution or Many Solutions5 min

2.5.2. Example 1 7 min

2.5.3. Example 2 4 min

2.5.4. Practice4 min

2.6.1. Solving Linear Systems5 min

2.6.2. Homogeneous Systems2 min

2.7.1. Geometric Interpretation of Solutions to SLEs4 min

2.7.2. Example3 min

2.7.3. Practice3 min

3. Linear Algebra (Matrix Algebra, Determinant, Inverse, and Applications)

4hr

3.I. Chapter Intro

3.1.1. Basics of Matrices3 min

3.1.2. Matrix Arithmetic3 min

3.1.3. Example1 min

3.1.4. Practice2 min

3.2.1. Augmented Matrix3 min

3.3.1. Echelon Forms5 min

3.4.1. Reducing a Matrix5 min

3.5.1. Matrix Addition (and Subtraction)3 min

3.5.2. Matrix Addition and Scalar Multiplication22 min

3.5.3. Matrix Addition and Scalar Multiplication

3.6.1. Matrix Multiplication6 min

3.7.1. Matrix Transpose3 min

3.7.2. Symmetric Matrices3 min

3.7.3. Example3 min

3.7.4. Practice60 sec

3.7.5. Practice2 min

3.8.1. Matrix Inverse4 min

3.8.2. Example3 min

3.8.3. Practice32 sec

3.8.4. Practice2 min

3.9.1. Matrix Inverse Algorithm3 min

3.9.2. Example2 min

3.9.3. Example2 min

3.9.4. Practice2 min

3.10.1. Solving Matrix Equations2 min

3.10.2. Example52 sec

3.10.3. Example4 min

3.10.4. Practice2 min

3.10.5. Practice54 sec

3.10.6. Practice2 min

3.11.1. Basics of Determinants5 min

3.11.2. Example2 min

3.11.3. Practice2 min

3.11.4. Practice3 min

3.12.1. Determinant & EROs3 min

3.12.2. Example2 min

3.12.3. Practice2 min

3.13.1. Minors and Cofactors4 min

3.13.2. Determinants of Large Matrices4 min

3.13.3. Example3 min

3.13.4. Practice2 min

3.13.5. Practice4 min

3.14.1. Determinants and Inverse3 min

3.14.2. Example3 min

3.14.3. Practice2 min

3.15.1. Markov Chains (Random Walks)7 min

3.15.2. Example6 min

3.15.3. Practice5 min

3.16.1. Least Squares Approximation6 min

3.16.2. Example4 min

3.16.3. Example: Least Squares for Polynomials

3.16.4. Practice

3.17.1. Cramer's Rule3 min

3.17.2. Example2 min

3.17.3. Practice3 min

4. Differential Calculus (Limits, Continuity, and Rate of Change)

1.8hr

4.1.1. Limit Basics2 min

4.1.2. Example1 min

4.2.1. Limit Laws 2 min

4.2.2. Practice1 min

4.3.1. One-Sided Limits2 min

4.3.2. Example: One-Sided Limit2 min

4.3.3. Practice: One-Sided Limits3 min

4.4.1. Infinite Limits2 min

4.4.2. Example1 min

4.4.3. Example3 min

4.5.1. Limits at Infinity3 min

4.5.2. Example60 sec

4.5.3. Example3 min

4.5.4. Example4 min

4.5.5. Practice 3 min

4.5.6. Practice3 min

4.6.1. Indeterminate Forms50 sec

4.7.1. Computing Limits by Factoring1 min

4.7.2. Example1 min

4.7.3. Practice2 min

4.8.1. Computing Limits by Multiplying by the Conjugate3 min

4.8.2. Example3 min

4.8.3. Practice3 min

4.9.1. Computing Limits by Getting a Common Denominator1 min

4.9.2. Example2 min

4.9.3. Practice4 min

4.10.1. Continuity2 min

4.10.2. Example2 min

4.10.3. Practice4 min

4.11.1. Average Rate of Change & the Secant Line2 min

4.11.2. Example

4.11.3. Practice Level 12 min

4.11.4. Practice Level 2

4.11.5. Practice Level 3

4.12.1. Derivatives as a Rate of Change2 min

4.12.2. Average Rate of Change46 sec

4.12.3. Example2 min

4.12.4. Practice1 min

4.13.1. The Limit Definition of a Derivative2 min

4.13.2. Example3 min

4.13.3. Practice5 min

4.13.4. When is Function Not Differentiable?

5. Differential Calculus (Derivative Rules, and Tangent Lines)

2hr

5.1.1. Differentiation Laws51 sec

5.2.1. The Power Rule1 min

5.2.2. Example2 min

5.2.3. Practice51 sec

5.3.1. The Product Rule49 sec

5.3.2. Example2 min

5.3.3. Example2 min

5.3.4. Practice2 min

5.4.1. The Quotient Rule1 min

5.4.2. Example2 min

5.4.3. Practice4 min

5.5.1. The Chain Rule1 min

5.5.2. Example2 min

5.5.3. Practice3 min

5.6.1. Derivatives of Exponential Functions1 min

5.6.2. Example52 sec

5.6.3. Example3 min

5.6.4. Practice1 min

5.7.1. Derivatives of Logarithmic Functions1 min

5.7.2. Example56 sec

5.7.3. Example2 min

5.7.4. Practice2 min

5.7.5. Practice: Log and Ln2 min

5.8.1. Implicit Differentiation2 min

5.8.2. Example3 min

5.8.3. Example3 min

5.8.4. Practice3 min

5.9.1. L’Hopital’s Rule2 min

5.9.2. Example2 min

5.9.3. Practice5 min

5.10.1. Derivatives of Inverse Functions52 sec

5.10.2. Example2 min

5.10.3. Practice3 min

5.11.1. Tangent Lines1 min

5.11.2. Example3 min

5.11.3. Practice2 min

5.12.1. Normal Lines1 min

5.12.2. Example3 min

5.12.3. Practice1 min

6. Differential Calculus (Applications of Derivatives)

4hr

6.1.1. Critical Points and Extrema2 min

6.1.2. Example

6.1.3. Practice3 min

6.2.1. Intervals of Increase and Decrease1 min

6.2.2. Example2 min

6.2.3. Practice3 min

6.3.1. Maximum and Minimum on Closed Intervals2 min

6.3.2. Example4 min

6.3.3. Practice3 min

6.3.4. Practice3 min

6.4.1. Higher Order Derivatives2 min

6.4.2. Example3 min

6.4.3. Practice2 min

6.4.4. Practice2 min

6.5.1. Concavity and Inflection Points56 sec

6.5.2. Example6 min

6.5.3. Practice6 min

6.6.1. 1st and 2nd Derivative Tests3 min

6.6.2. Example7 min

6.6.3. Example

6.6.4. Practice3 min

6.7.1. Curve Sketching2 min

6.7.2. Example7 min

6.7.3. Practice9 min

6.7.4. Practice

6.8.1. Related Rates1 min

6.9.1. Elasticity of Demand2 min

6.9.2. Example3 min

6.9.3. Practice: Elasticity of Demand4 min

6.10.1. Cost, Revenue, and Profit2 min

6.10.2. Example3 min

6.10.3. Practice2 min

6.10.4. Practice4 min

6.11.1. Optimization1 min

6.11.2. Example4 min

6.11.3. Example4 min

6.11.4. Practice6 min

6.11.5. Practice4 min

6.12.1. Related Rates

6.12.2. Related Rates5 min

6.12.3. Related Rates5 min

6.12.4. Linear Approximation4 min

6.12.5. Linear Approximation

6.12.6. Taylor Series from Definition7 min

6.12.7. Taylor Polynomials

6.12.8. Maclaurin Polynomial

6.12.9. Newton's Method2 min

6.12.10. Newton's Method

6.12.11. L'Hopital's Rule

6.12.12. L'Hopital's Rule

6.12.13. L'Hopital's Rule

6.12.14. Limits

6.12.15. L'Hopital's Rule

6.12.16. L'Hopital's Rule

6.12.17. Limits

6.12.18. Limits

6.12.19. Extreme Value Theorem

6.12.20. Rolle's Theorem1 min

6.12.21. Rolle's Theorem6 min

6.12.26. Intervals of Increase and Decrease

6.12.27. Intervals of Increase and Decrease3 min

6.12.28. Critical Points6 min

6.12.29. Critical Points1 min

6.12.30. Extrema5 min

6.12.31. Extrema6 min

6.12.32. Second Derivative Test10 min

6.12.33. Curve Sketching

6.12.34. Curve Sketching12 min

6.12.35. Curve Sketching

6.12.36. Optimization

6.12.37. Optimization

6.12.38. Optimization

7. Integral Calculus (Rules of Integration)

2hr

7.1.1. Antiderivatives (Indefinite Integral)3 min

7.2.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

7.2.2. Example42 sec

7.2.3. Practice1 min

7.2.4. Practice2 min

7.3.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

7.3.2. Example2 min

7.3.3. Practice1 min

7.4.1. Initial Conditions2 min

7.4.2. Example2 min

7.4.3. Practice5 min

7.5.1. Integration by Substitution2 min

7.5.2. Example4 min

7.5.3. Example3 min

7.5.4. Example (w/ Back-Substitution)4 min

7.5.5. Practice

7.5.6. Practice

7.5.7. Practice

7.5.8. Practice (w/ Back-Substitution)

7.6.1. The Definite Integrals & Area Under a Curve2 min

7.6.2. Example7 min

7.6.3. Practice2 min

7.6.4. Practice12 min

7.7.1. Properties of the Definite Integral2 min

7.7.2. Practice2 min

7.7.3. Practice2 min

7.8.1. Computing Definite Integrals Geometrically44 sec

7.8.2. Example1 min

7.8.3. Practice1 min

7.9.1. Fundamental Theorem of Calculus - Part I2 min

7.10.1. Fundamental Theorem of Calculus - Part 21 min

7.10.2. Example2 min

7.10.3. Example

7.10.4. Practice 4 min

7.10.5. Practice3 min

7.10.6. Practice1 min

8. Integral Calculus (Techniques of Integration, and Applications)

1.9hr

8.1.1. Integration by Substitution2 min

8.1.2. Example4 min

8.1.3. Example3 min

8.1.4. Example (w/ Back-Substitution)4 min

8.1.5. Practice

8.1.6. Practice

8.1.7. Practice

8.1.8. Practice (w/ Back-Substitution)

8.2.1. Integration by Parts3 min

8.3.1. Area between curves1 min

8.3.2. Example5 min

8.3.3. Example5 min

8.3.4. Practice

8.4.1. Average Value of a Function47 sec

8.4.2. Example2 min

8.4.3. Practice2 min

8.5.1. Distance and Displacement (Net Change Theorem)2 min

8.5.2. Example6 min

8.5.3. Practice

8.5.4. Practice

9. Functions of Several Variables

1.8hr

9.1.1. Functions of Several Variables5 min

9.1.2. Practice3 min

9.2.1. Functions of 2 & 3 Variables and Contour Curves5 min

9.2.2. Contour Diagram3 min

9.2.3. Practice Question1 min

9.2.4. Practice: Match the map with the equation9 min

9.3.1. Partial derivatives6 min

9.3.2. Example: Partial derivatives3 min

9.3.3. Practice: First Partial derivatives2 min

9.3.4. Practice: Second Partial Derivatives3 min

9.4.1. Chain Rule7 min

9.4.2. Example: Chain Rule (1)2 min

9.4.3. Example: Chain Rule (2)1 min

9.4.4. Practice: Chain Rule2 min

9.4.5. Practice: Chain Rule2 min

9.4.6. Practice: Chain Rule*3 min

9.4.7. Implicit Differentiation2 min

9.5.1. Differentials4 min

9.5.2. Practice: Differentials

9.5.3. Practice: Differentials

9.6.1. Maximums, Minimums, and Critical Points5 min

9.7.1. Local Max & Min4 min

9.7.2. Absolute Max & Min5 min

9.7.3. Lagrange Multipliers3 min

9.7.4. Practice: Lagrange Multipliers

9.7.5. Practice: Lagrange Multipliers

9.8.1. Lagrange Multipliers3 min

Mock Exam

ME.1. Final Exam - Mock Assessment24 Qns

ADM 1305

Course Overview

1. Functions

2. Linear Algebra (Systems of Linear Equations)

3. Linear Algebra (Matrix Algebra, Determinant, Inverse, and Applications)

4. Differential Calculus (Limits, Continuity, and Rate of Change)

5. Differential Calculus (Derivative Rules, and Tangent Lines)

6. Differential Calculus (Applications of Derivatives)

7. Integral Calculus (Rules of Integration)

8. Integral Calculus (Techniques of Integration, and Applications)

9. Functions of Several Variables

Mock Exam

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