MATH 1LS3

Mac

Course Overview

Grade Boosters

Lessons & Practice

I. Welcome

1. Chapter 1: Introduction to Models and Functions

2.8hr

1.1.1. Basic Functions & Their Graphs14 min

1.2.1. Inverse Functions3 min

1.2.2. Example3 min

1.2.3. Practice Level 12 min

1.2.4. Practice Level 21 min

1.2.5. Practice Level 32 min

1.3.1. Reciprocal Functions2 min

1.3.2. Graphing Reciprocal Functions7 min

1.3.3. Example4 min

1.3.4. Example5 min

1.3.5. Example3 min

1.3.6. Practice Level 12 min

1.3.7. Practice Level 23 min

1.3.8. Practice Level 33 min

1.4.1. Radical Functions59 sec

1.5.1. Rational Functions4 min

1.5.2. Example3 min

1.5.3. Example2 min

1.5.4. Example3 min

1.5.5. Practice Level 12 min

1.5.6. Practice Level 22 min

1.5.7. Practice Level 3

1.6.1. Example3 min

1.6.2. Practice Level 11 min

1.6.3. Practice Level 22 min

1.7.1. Example3 min

1.7.2. Practice Level 12 min

1.7.3. Practice Level 23 min

1.7.4. Practice Level 35 min

1.8.1. Vertical Translations2 min

1.8.2. Horizontal Translations3 min

1.8.3. Example 3 min

1.8.4. Example 4 min

1.8.5. Example3 min

1.8.6. Practice Level 12 min

1.8.7. Practice Level 21 min

1.8.8. Practice Level 32 min

1.9.1. Vertical Reflections1 min

1.9.2. Horizontal Reflections2 min

1.9.3. Example3 min

1.9.4. Example3 min

1.9.5. Example3 min

1.9.6. Practice Level 12 min

1.9.7. Practice Level 22 min

1.9.8. Practice Level 32 min

1.10.1. Vertical Expansions & Compressions3 min

1.10.2. Horizontal Expansions & Compressions2 min

1.10.3. Example7 min

1.10.4. Example3 min

1.10.5. Practice Level 11 min

1.10.6. Practice Level 23 min

1.10.7. Practice Level 3

1.11.1. Combining Transformations4 min

1.11.2. Example1 min

1.11.3. Practice Level 12 min

1.11.4. Practice Level 23 min

1.11.5. Practice Level 34 min

1.12.1. Inverse Functions & Transformations5 min

1.12.2. Example

1.12.3. Practice Level 131 sec

1.12.4. Practice Level 23 min

1.12.5. Practice Level 33 min

2. Chapter 2: Modelling Using Elementary Functions

2.5hr

2.1.1. Relations5 min

2.1.2. Linear Relations6 min

2.1.3. Example8 min

2.1.4. Practice Level 14 min

2.1.5. Practice Level 27 min

2.2.1. Linear Equations4 min

2.2.2. Practice Level 113 min

2.2.3. Practice Level 27 min

2.2.4. Parallel & Perpendicular Lines7 min

2.2.5. Practice Level 35 min

2.3.1. Example: Power functions2 min

2.4.1. Exponential Functions3 min

2.4.2. Example1 min

2.4.3. Example2 min

2.5.1. Logarithmic Functions4 min

2.5.2. Example3 min

2.5.3. Example:3 min

2.5.4. Practice2 min

2.6.1. Semi Log Graphs2 min

2.6.2. Practice: semi-log graph6 min

2.7.1. Inverse Functions3 min

2.7.2. Example3 min

2.7.3. Practice2 min

2.8.1. Trigonometric Ratios in Radians9 min

2.8.2. Example4 min

2.8.3. Practice Level 13 min

2.8.4. Practice Level 22 min

2.8.5. Practice Level 32 min

2.9.1. Trigonometric Functions6 min

2.9.2. Example4 min

2.9.3. Trig Identities2 min

2.9.4. Practice3 min

2.9.5. Practice4 min

2.10.1. Inverse Trigonometric Functions4 min

2.10.2. Example3 min

2.10.3. Practice2 min

2.10.4. Practice2 min

3. Chapter 3: Discrete-Time Dynamical Systems

26min

3.1.1. Discrete Dynamical Systems

3.2.1. How to model a discrete dynamical system1 min

3.2.2. Solving a Discrete Time dynamical System3 min

3.2.3. Manipulation of the Update Function2 min

3.2.4. Example: Dynamical System 12 min

3.2.5. Example: Dynamical System 247 sec

3.2.6. Example: Dynamical System 32 min

3.2.7. Example: Dynamical System 452 sec

3.3.1. Introduction to cobwebbing4 min

3.3.2. Equilibria3 min

3.3.3. Example: Equilibria and cowebbing2 min

3.3.6. Practice: Equilibria and cowebbing6 min

3.3.7. Practice

3.3.8. Practice

3.3.9. Practice

3.3.10. Practice

4. Chapter 4: Limits, Continuity & Derivatives

1.7hr

4.1.1. Average and Instanteous Rate of Change6 min

4.1.2. Instantaneous Rate of Change & the Tangent Line2 min

4.1.3. Average & Instantaneous Rate of Change

4.1.4. Instantaneous rate of change

4.1.5. Practice Level 3

4.2.1. Limit Basics2 min

4.2.2. Example1 min

4.3.1. Limit Laws 2 min

4.3.2. Practice1 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. Continuity2 min

4.6.2. Example2 min

4.6.3. Practice4 min

4.7.1. L’Hopital’s Rule2 min

4.7.2. Example2 min

4.7.3. Practice5 min

4.8.1. Computing Limits by Factoring1 min

4.8.2. Example1 min

4.8.3. Practice2 min

4.9.1. Computing Limits by Multiplying by the Conjugate3 min

4.9.2. Example3 min

4.9.3. Practice3 min

4.10.1. Computing Limits by Getting a Common Denominator1 min

4.10.2. Example2 min

4.10.3. Practice4 min

4.11.1. The Definition of a Derivative

4.11.2. Example: Definition of a Derivative5 min

4.11.3. When is Function Not Differentiable?

5. Chapter 5: Differentiation Rules and Working with Derivatives

2.6hr

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. Derivatives of Exponential Functions1 min

5.3.2. Example52 sec

5.3.3. Example3 min

5.3.4. Practice1 min

5.4.1. The Product Rule49 sec

5.4.2. Example2 min

5.4.3. Example2 min

5.4.4. Practice2 min

5.5.1. The Quotient Rule1 min

5.5.2. Example2 min

5.5.3. Practice4 min

5.6.1. The Chain Rule1 min

5.6.2. Example2 min

5.6.3. Practice3 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. Derivatives of Trigonometric Functions1 min

5.8.2. Example39 sec

5.8.3. Example3 min

5.8.4. Example1 min

5.8.5. Practice3 min

5.8.6. Practice2 min

5.9.1. Derivatives of Inverse Functions52 sec

5.9.2. Example2 min

5.9.3. Practice3 min

5.10.1. Implicit Differentiation2 min

5.10.2. Example3 min

5.10.3. Example3 min

5.10.4. Practice3 min

5.11.1. Logarithmic Differentiation2 min

5.11.2. Example2 min

5.11.3. Practice3 min

5.12.1. Higher Order Derivatives2 min

5.12.2. Example3 min

5.12.3. Practice2 min

5.12.4. Practice2 min

5.13.1. Inverse Trig Derivatives1 min

5.13.2. Example1 min

5.13.3. Practice3 min

5.14.1. Tangent Lines1 min

5.14.2. Example3 min

5.14.3. Practice2 min

5.15.1. Taylor Polynomials 1 min

5.15.2. Example6 min

5.15.3. Example4 min

5.15.4. Practice

5.16.1. Taylor Polynomial Remainder2 min

5.16.2. Example3 min

5.16.3. Practice

6. Chapter 6: Applications of Derivatives

5hr

6.1.1. Extreme Value Theorem1 min

6.2.1. Maximum and Minimum on Closed Intervals2 min

6.2.2. Example4 min

6.2.3. Practice3 min

6.2.4. Practice3 min

6.3.1. Intermediate Value Theorem

6.3.2. Example: Intermediate Value Theorem1 min

6.3.3. New Practice Question

6.3.4. New Practice Question

6.4.1. The Mean Value Theorem1 min

6.4.2. Example2 min

6.4.3. Practice2 min

6.5.1. Rolle's Theorem1 min

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Fermat's Theorem47 sec

6.7.1. Newton's Method1 min

6.7.3. Example4 min

6.7.4. Practice

6.7.5. Practice2 min

6.8.1. L’Hopital’s Rule2 min

6.8.2. Example2 min

6.8.3. Practice5 min

6.9.1. Curve Sketching2 min

6.9.2. Example7 min

6.9.3. Practice9 min

6.9.4. Practice

6.10.1. Solving General Indeterminate Forms2 min

6.10.2. Example2 min

6.10.3. Practice5 min

6.10.4. Practice2 min

6.11.1. Intervals of Increase and Decrease1 min

6.11.2. Example2 min

6.11.3. Practice3 min

6.12.1. Critical Points and Extrema2 min

6.12.2. Example

6.12.3. Practice3 min

6.13.1. 1st and 2nd Derivative Tests3 min

6.13.2. Example7 min

6.13.3. Example

6.13.4. Practice3 min

6.14.1. Concavity and Inflection Points56 sec

6.14.2. Example6 min

6.14.3. Practice6 min

6.15.1. Optimization1 min

6.15.2. Example4 min

6.15.3. Example4 min

6.15.4. Practice6 min

6.15.5. Practice4 min

6.16.1. Differential Equations8 min

6.16.2. Direction Fields/Slope Fields5 min

6.16.3. Practice Question: DE Solution Graphs3 min

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

6.16.5. Practice

6.17.1. Separable First Order Differential Equations3 min

6.17.2. Practice (separable DE)2 min

6.17.3. Practice (IVP)3 min

6.17.4. Practice (IVP)3 min

6.17.5. Practice (IVP*)5 min

6.17.6. Practice (separable DE)1 min

6.18.1. Linear First Order Differential Equations7 min

6.18.2. Practice (integrating factor)1 min

6.18.3. Practice (linear DE)3 min

6.18.4. Practice (IVP)3 min

6.18.5. Practice (IVP)4 min

6.19.1. Common DE Applications (Word Problems)

6.19.2. Practice (population)3 min

6.19.3. Practice (population)4 min

6.19.4. Practice (cooling & heating)3 min

6.19.5. Practice (mixing tank)6 min

6.19.6. Practice (mixing tank)8 min

6.20.1. Related Rates

6.20.2. Related Rates5 min

6.20.3. Related Rates5 min

6.20.4. Linear Approximation4 min

6.20.5. Linear Approximation

6.20.6. Taylor Series from Definition7 min

6.20.7. Taylor Polynomials

6.20.8. Maclaurin Polynomial

6.20.9. Newton's Method2 min

6.20.10. Newton's Method

6.20.11. L'Hopital's Rule

6.20.12. L'Hopital's Rule

6.20.13. L'Hopital's Rule

6.20.14. Limits

6.20.15. L'Hopital's Rule

6.20.16. L'Hopital's Rule

6.20.17. Limits

6.20.18. Limits

6.20.19. Extreme Value Theorem

6.20.20. Rolle's Theorem1 min

6.20.21. Rolle's Theorem6 min

6.20.23. MVT2 min

6.20.24. MVT3 min

6.20.26. Intervals of Increase and Decrease

6.20.27. Intervals of Increase and Decrease3 min

6.20.28. Critical Points6 min

6.20.29. Critical Points1 min

6.20.30. Extrema5 min

6.20.31. Extrema6 min

6.20.32. Second Derivative Test10 min

6.20.33. Curve Sketching

6.20.34. Curve Sketching12 min

6.20.35. Curve Sketching

6.20.36. Optimization

6.20.37. Optimization

6.20.38. Optimization

7. Chapter 7: Integrals and Applications

4hr

7.1.1. Antiderivatives (Indefinite Integral)3 min

7.1.2. Example2 min

7.1.3. Practice1 min

7.1.4. Practice1 min

7.1.5. Practice1 min

7.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

7.2.2. Example1 min

7.2.3. Practice1 min

7.2.4. Practice1 min

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

7.3.2. Example1 min

7.3.3. Practice1 min

7.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

7.4.2. Example42 sec

7.4.3. Practice1 min

7.4.4. Practice2 min

7.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

7.5.2. Example2 min

7.5.3. Practice1 min

7.6.1. Initial Conditions2 min

7.6.2. Example2 min

7.6.3. Practice5 min

7.7.1. Approximating Areas & Riemann Sums 3 min

7.7.2. Example4 min

7.7.3. Practice3 min

7.8.1. The Definite Integrals & Area Under a Curve2 min

7.8.2. Example7 min

7.8.3. Practice2 min

7.8.4. Practice12 min

7.9.1. Properties of the Definite Integral2 min

7.9.2. Practice2 min

7.9.3. Practice2 min

7.10.1. Integration by Substitution2 min

7.10.2. Example4 min

7.10.3. Example3 min

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

7.10.5. Practice

7.10.6. Practice

7.10.7. Practice

7.10.8. Practice (w/ Back-Substitution)

7.11.1. Integration by Parts5 min

7.11.2. Example: Integration by Parts4 min

7.11.3. Example: Integration by parts3 min

7.11.4. Example: Integration by parts5 min

7.11.5. Practice: Integration by Parts2 min

7.12.1. Improper Integrals5 min

7.12.2. Example: Improper Type 13 min

7.12.3. Example: Improper Type 23 min

7.12.4. Concept Clarifier: Improper Integrals3 min

7.12.5. Practice: Improper Integrals3 min

7.13.1. Fundamental Theorem of Calculus - Part I2 min

7.13.2. Example1 min

7.13.3. Example48 sec

7.13.4. Practice1 min

7.13.5. Practice2 min

7.14.1. Fundamental Theorem of Calculus - Part 21 min

7.14.2. Example2 min

7.14.3. Example

7.14.4. Practice 4 min

7.14.5. Practice3 min

7.14.6. Practice1 min

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

7.15.2. Example6 min

7.15.3. Practice

7.15.4. Practice

7.16.1. Average Value of a Function47 sec

7.16.2. Example2 min

7.16.3. Practice2 min

7.17.1. Area between curves1 min

7.17.2. Example5 min

7.17.3. Example5 min

7.17.4. Practice

7.18.1. Volumes of Revolution by Cross Sections (Washers)3 min

7.18.2. Example4 min

7.18.3. Example3 min

7.18.4. Practice

7.18.5. Practice

7.19.1. Volumes of Revolution by Cylindrical Shells2 min

7.19.2. Practice

7.19.3. Practice

7.20.1. Arc Length41 sec

7.20.2. Example3 min

7.20.3. Practice4 min

7.21.1. Surface Area of Revolution1 min

7.21.2. Example5 min

7.21.3. Practice

7.22.1. Position, Velocity, and Acceleration1 min

7.22.2. Example2 min

7.22.3. Example4 min

7.22.4. Practice3 min

7.23.1. Mass and Density60 sec

7.23.2. Example3 min

7.23.3. Practice

Mock Exams

ME.1. Test 2 - Mock Assessment18 Qns

ME.2. Test 3 - Mock Assessment17 Qns

ME.3. Final Exam - Mock Assessment34 Qns

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Welcome to Calculus for the Life Sciences!
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