MATH 156

U of A

Course Overview

Lessons & Practice

I. Welcome

1. Review of Derivatives

2hr

1.1.1. The Limit Definition of a Derivative2 min

1.1.2. Example3 min

1.1.3. Practice5 min

1.1.4. When is Function Not Differentiable?

1.2.1. Differentiation Laws51 sec

1.3.1. The Power Rule1 min

1.3.2. Example2 min

1.3.3. Practice51 sec

1.4.1. The Product Rule49 sec

1.4.2. Example2 min

1.4.3. Example2 min

1.4.4. Practice2 min

1.5.1. The Quotient Rule1 min

1.5.2. Example2 min

1.5.3. Practice4 min

1.6.1. The Chain Rule1 min

1.6.2. Example2 min

1.6.3. Practice3 min

1.7.1. Derivatives of Trigonometric Functions1 min

1.7.2. Example39 sec

1.7.3. Example3 min

1.7.4. Example1 min

1.7.5. Practice3 min

1.7.6. Practice2 min

1.8.1. Derivatives of Exponential Functions1 min

1.8.2. Example52 sec

1.8.3. Example3 min

1.8.4. Practice1 min

1.9.1. Derivatives of Logarithmic Functions1 min

1.9.2. Example56 sec

1.9.3. Example2 min

1.9.4. Practice2 min

1.9.5. Practice: Log and Ln2 min

1.10.1. Inverse Trig Derivatives1 min

1.10.2. Example1 min

1.10.3. Practice3 min

1.11.1. Higher Order Derivatives2 min

1.11.2. Example3 min

1.11.3. Practice2 min

1.11.4. Practice2 min

2. Review of Integration

2.3hr

2.1.1. Antiderivatives (Indefinite Integral)3 min

2.1.2. Example2 min

2.1.3. Practice1 min

2.1.4. Practice1 min

2.1.5. Practice1 min

2.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

2.2.2. Example1 min

2.2.3. Practice1 min

2.2.4. Practice1 min

2.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

2.3.2. Example1 min

2.3.3. Practice1 min

2.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

2.4.2. Example42 sec

2.4.3. Practice1 min

2.4.4. Practice2 min

2.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2.5.2. Example2 min

2.5.3. Practice1 min

2.6.1. Initial Conditions2 min

2.6.2. Example2 min

2.6.3. Practice5 min

2.7.1. Finite Sums & Summation Notation3 min

2.7.2. Example5 min

2.7.3. Practice4 min

2.7.4. Practice4 min

2.8.1. Approximating Areas & Riemann Sums 3 min

2.8.2. Example4 min

2.8.3. Practice3 min

2.9.1. The Definite Integrals & Area Under a Curve2 min

2.9.2. Example7 min

2.9.3. Practice2 min

2.9.4. Practice12 min

2.10.1. Properties of the Definite Integral2 min

2.10.2. Practice2 min

2.10.3. Practice2 min

2.11.1. Computing Definite Integrals Geometrically44 sec

2.11.2. Example1 min

2.11.3. Practice1 min

2.12.1. Fundamental Theorem of Calculus - Part I2 min

2.12.2. Example1 min

2.12.3. Example48 sec

2.12.4. Practice1 min

2.12.5. Practice2 min

2.13.1. Fundamental Theorem of Calculus - Part 21 min

2.13.2. Example2 min

2.13.3. Example

2.13.4. Practice 4 min

2.13.5. Practice3 min

2.13.6. Practice1 min

2.14.1. Average Value of a Function47 sec

2.14.2. Example2 min

2.14.3. Practice2 min

2.15.1. Area between Curves3 min

2.15.2. Practice4 min

2.15.3. Practice3 min

2.15.4. Practice (multiple regions)4 min

3. Chapter 1: Integration Techniques

2.6hr

3.1.1. Integration by Substitution2 min

3.1.2. Example4 min

3.1.3. Example3 min

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

3.1.5. Practice

3.1.6. Practice

3.1.7. Practice

3.1.8. Practice (w/ Back-Substitution)

3.2.1. Integration by Parts3 min

3.2.2. Example5 min

3.2.3. Example3 min

3.2.4. Example6 min

3.2.5. Practice

3.2.6. Practice

3.3.1. Improper Integrals4 min

3.3.2. Practice (type 1)2 min

3.3.3. Practice (type 1)5 min

3.3.4. Practice (Type 2)5 min

3.4.1. Comparison Theorem for Improper Integrals3 min

3.4.2. Practice (type 1 - converges)3 min

3.4.3. Practice (type 2 - converges)4 min

3.4.4. Practice (type 2 - diverges)

3.5.1. L’Hopital’s Rule2 min

3.5.2. Example2 min

3.5.3. Practice5 min

3.6.1. Taylor Polynomials 1 min

3.6.2. Example6 min

3.6.3. Example4 min

3.6.4. Practice

3.7.1. Related Rates

3.7.2. Related Rates5 min

3.7.3. Related Rates5 min

3.7.4. Linear Approximation4 min

3.7.5. Linear Approximation

3.7.6. Taylor Series from Definition7 min

3.7.7. Taylor Polynomials

3.7.8. Maclaurin Polynomial

3.7.9. Newton's Method2 min

3.7.10. Newton's Method

3.7.11. L'Hopital's Rule

3.7.12. L'Hopital's Rule

3.7.13. L'Hopital's Rule

3.7.15. L'Hopital's Rule

3.7.16. L'Hopital's Rule

3.7.19. Extreme Value Theorem

3.7.20. Rolle's Theorem1 min

3.7.21. Rolle's Theorem6 min

3.7.23. MVT2 min

3.7.24. MVT3 min

3.7.26. Intervals of Increase and Decrease

3.7.27. Intervals of Increase and Decrease3 min

3.7.28. Critical Points6 min

3.7.29. Critical Points1 min

3.7.30. Extrema5 min

3.7.31. Extrema6 min

3.7.32. Second Derivative Test10 min

3.7.33. Curve Sketching

3.7.34. Curve Sketching12 min

3.7.35. Curve Sketching

3.7.36. Optimization

3.7.37. Optimization

3.7.38. Optimization

4. Chapter 2: Partial Derivatives

1.3hr

4.1.1. Functions of Several Variables5 min

4.1.2. Practice3 min

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

4.2.2. Contour Diagram3 min

4.2.3. Practice Question1 min

4.2.4. Practice: Match the map with the equation9 min

4.3.1. Partial derivatives6 min

4.3.2. Example: Partial derivatives3 min

4.3.3. Practice: First Partial derivatives2 min

4.3.4. Practice: Second Partial Derivatives3 min

4.4.1. Tangent plane3 min

4.4.2. Example: Tangent Planes (2)3 min

4.4.3. Practice: Tangent Plane

4.4.4. Linear (Tangent Plane) Approximation3 min

4.4.5. Practice: Linear approximation

4.5.1. Chain Rule7 min

4.5.2. Example: Chain Rule (1)2 min

4.5.3. Example: Chain Rule (2)1 min

4.5.4. Practice: Chain Rule2 min

4.5.5. Practice: Chain Rule2 min

4.5.6. Practice: Chain Rule*3 min

4.5.7. Implicit Differentiation2 min

4.6.1. Gradient and directional derivative7 min

4.6.2. Directional Derivative 2 min

4.6.3. Gradient and Directional Derivative1 min

4.6.4. Concept Clarifier2 min

4.6.5. Practice: Gradient and directional derivative

5. Chapter 3: Multivariate Optimization

1.4hr

5.1.1. Maximums, Minimums, and Critical Points5 min

5.1.2. Example5 min

5.1.3. Example5 min

5.1.4. Practice4 min

5.1.5. Practice3 min

5.2.1. Local Max & Min4 min

5.2.2. Absolute Max & Min5 min

5.2.3. Lagrange Multipliers3 min

5.2.4. Practice: Lagrange Multipliers

5.2.5. Practice: Lagrange Multipliers

5.3.1. Lagrange Multipliers3 min

5.3.2. Example3 min

5.3.4. Practice3 min

5.3.5. Practice4 min

5.4.1. Differentials4 min

5.4.2. Practice: Differentials

5.4.3. Practice: Differentials

5.5.1. Introduction to Multiple Integrals1 min

5.6.1. Double Integrals over Rectangular Regions4 min

5.6.2. Example: Double Integrals over Rectangular Regions (1)2 min

5.6.3. Example: Double Integrals over Rectangular Regions (2)5 min

5.6.4. Example: Iterated Integrals (1)4 min

5.7.1. Double Integrals over General Regions1 min

5.7.2. Example: Double Integrals over General Regions (1)5 min

5.7.3. Example: Double Integrals over General Regions (2)2 min

5.7.4. Practice: Double Integrals over General Regions (1)3 min

5.7.5. Practice: Double Integrals over General Regions (2)5 min

6. Chapter 4: Probability and Calculus

4hr

6.1.1. Events & Sample Spaces6 min

6.1.2. Types of Probability6 min

6.1.3. Probability Language & Notation4 min

6.1.4. Example3 min

6.1.5. Independent vs. Mutually Exclusive Events4 min

6.1.6. Example2 min

6.1.7. Practice

6.2.1. Interpretation of Probability2 min

6.2.2. Complement Rule3 min

6.2.3. Practice1 min

6.2.4. The Addition Rule4 min

6.3.1. Probability of Independent Events4 min

6.3.2. Example3 min

6.3.3. Practice2 min

6.4.1. Probability of Dependent Events (Conditional Probability)7 min

6.4.2. Conditional Probability: Tree Diagram5 min

6.4.3. Bayes’ Theorem4 min

6.4.4. Example4 min

6.4.5. Practice3 min

6.5.1. Cumulative Distribution Function (CDF)3 min

6.5.2. Example6 min

6.5.3. Practice2 min

6.6.1. Combining Random Variables7 min

6.6.2. Example2 min

6.6.3. Practice2 min

6.6.4. Example3 min

6.6.5. Practice

6.6.6. Functions of Two Independent Random Variables X and Y5 min

6.6.7. Example3 min

6.6.8. Practice

6.6.9. Practice2 min

6.7.1. Conditional Probability & Joint Distribution7 min

6.7.2. Example5 min

6.7.3. Practice

6.7.4. Random Variables & Joint Distribution7 min

6.7.5. Example3 min

6.7.6. Practice

6.7.8. Practice

6.8.1. Bernoulli Trials4 min

6.8.2. Practice4 min

6.8.3. Binomial Experiment4 min

6.8.4. Binomial Distribution8 min

6.8.5. Example10 min

6.8.6. Example1 min

6.8.7. Practice6 min

6.8.8. Practice

6.9.1. Poisson Experiment5 min

6.9.2. Poisson Distribution1 min

6.9.3. Example3 min

6.9.4. Practice5 min

6.9.5. Practice5 min

6.10.1. Continuous Probability Distribution Theory10 min

6.11.1. Expected Value (Mean)3 min

6.11.2. Example: Expected Value3 min

6.11.3. Expected Value Example #42 min

6.12.1. Variance

\sigma^2

and Standard Deviation

\sigma

6.12.2. Variance and Standard Deviation

6.12.3. Variance and Standard Deviation 2 min

6.12.4. Question 647 sec

6.13.1. Normal Distribution11 min

6.13.2. Practice5 min

6.14.1. Distribution Functions4 min

6.14.2. Practice: PDF3 min

6.14.3. Practice: CDF2 min

6.14.4. Mean, Median, and Variance3 min

6.14.5. Practice2 min

6.14.6. Practice: Median1 min

7. Business Applications

3hr

7.1.1. Applications of Exponential Functions1 min

7.1.2. Example2 min

7.1.3. Practice Level 14 min

7.1.4. Practice Level 25 min

7.1.5. Practice Level 33 min

7.2.1. Cost, Price, Revenue, and Profit1 min

7.2.2. Supply and Demand2 min

7.2.3. Marginal & Average Cost, Revenue and Profit1 min

7.2.4. Example: Average Rate of Change of Cost2 min

7.2.5. Practice: Average Profit4 min

7.2.6. Example: Marginal Cost2 min

7.2.7. Practice: Marginal Revenue given Price Function2 min

7.2.8. Practice: Marginal Revenue and Profit7 min

7.3.1. Average Product and Marginal Product12 min

7.3.2. Example: Marginal and Average Product2 min

7.3.3. Practice: Marginal vs Average Product3 min

7.4.1. Simple Interest8 min

7.4.2. Example3 min

7.4.3. Practice Level 13 min

7.4.4. Practice Level 23 min

7.4.5. Practice Level 34 min

7.5.1. Compound Interest9 min

7.5.2. Example5 min

7.5.3. Example4 min

7.5.4. Practice Level 13 min

7.5.5. Practice Level 23 min

7.5.6. Practice Level 36 min

7.6.1. Present Value3 min

7.6.2. Example: Net Present Value6 min

7.6.3. Concept Clarifier: Net Present Value (NPV) 5 min

7.6.4. Practice: Present Value1 min

7.7.1. Time Value of Money27 min

7.7.2. Concept Clarifier: Annuity Due (Future Value)8 min

7.8.1. Investments and Loans with Regular Payments8 min

7.8.2. Example5 min

7.8.3. Example5 min

7.8.4. Practice Level 14 min

7.8.5. Practice Level 1 (Spreadsheets)

7.8.6. Practice Level 24 min

7.8.7. Practice Level 38 min

Mock Exams

ME.1. Midterm Exam - Mock Assessment12 Qns

ME.2. Final Exam - Mock Assessment23 Qns

I Welcome

Free Activity

Hi Math 156 students!

I'm Jess, and I'm here to help you learn the concepts in Math 156. I've put together the concepts that are generally covered in this course, but would love your help to make it even better and more tailored for this semester! If you're willing to help, please send me a direct message or let me know in the Ask a Question box. Thanks 🙏 and happy studying 😄

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