1. Pre-Calculus (Review)

3hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice2 min

1.1.5. Practice52 sec

1.2.4. Practice 40 sec

1.2.5. Practice 3 min

1.3.1. Operations with Functions3 min

1.3.2. Example2 min

1.3.3. Practice2 min

1.3.4. Practice1 min

1.4.1. Even and Odd Functions3 min

1.4.2. Example2 min

1.5.1. Transformation of Graphs2 min

1.5.2. Example1 min

1.5.3. Practice2 min

1.6.1. Basic of Polynomials4 min

1.6.2. Example2 min

1.6.3. Practice3 min

1.6.4. Polynomial Graphs & Characteristics4 min

1.6.5. Example2 min

1.6.6. Practice2 min

1.7.1. Factoring 5 min

1.7.2. Factoring a Difference & Sum of Cubes3 min

1.7.3. Example2 min

1.7.4. Practice46 sec

1.7.5. Practice2 min

1.7.6. Practice2 min

1.8.1. Dividing Polynomials - Long Division6 min

1.8.2. Example3 min

1.8.3. Dividing Polynomials - Synthetic Division8 min

1.8.4. Example2 min

1.8.5. Practice2 min

1.8.6. Practice3 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. Piecewise Functions4 min

1.11.2. Example5 min

1.11.3. Practice3 min

1.12.1. Absolute Value Function1 min

1.12.2. Example3 min

1.13.1. Inverse Functions3 min

1.13.2. Example3 min

1.13.3. Practice2 min

1.14.1. Exponential Functions3 min

1.14.2. Example1 min

1.14.3. Example2 min

1.15.1. Logarithmic Functions4 min

1.15.2. Example3 min

1.15.3. Example:3 min

1.15.4. Practice2 min

1.16.1. Trigonometric Functions6 min

1.16.2. Example4 min

1.16.3. Trig Identities2 min

1.16.4. Practice3 min

1.16.5. Practice4 min

1.17.1. Inverse Trigonometric Functions4 min

1.17.2. Example3 min

1.17.3. Practice2 min

1.17.4. Practice2 min

2. Limits

1.9hr

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. Infinite Limits2 min

2.4.2. Example1 min

2.4.3. Example3 min

2.5.1. Limits at Infinity3 min

2.5.2. Example60 sec

2.5.3. Example3 min

2.5.4. Example4 min

2.5.5. Practice 3 min

2.5.6. Practice3 min

2.6.1. Indeterminate Forms50 sec

2.7.1. Computing Limits by Factoring1 min

2.7.2. Example1 min

2.7.3. Practice2 min

2.8.1. Computing Limits by Multiplying by the Conjugate3 min

2.8.2. Example3 min

2.8.3. Practice3 min

2.9.1. Computing Limits by Getting a Common Denominator1 min

2.9.2. Example2 min

2.9.3. Practice4 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. The Squeeze Theorem2 min

2.11.2. Example2 min

2.11.3. Practice2 min

2.12.1. Continuity2 min

2.12.2. Example2 min

2.12.3. Practice4 min

2.13.1. The Intermediate Value Theorem2 min

2.13.2. Example2 min

2.13.3. Practice2 min

2.14.1. The Epsilon Delta Definition of a Limit

2.14.2. Example3 min

2.14.3. Practice

3. Derivatives

2.8hr

3.1.1. Derivatives as a Rate of Change2 min

3.1.2. Average Rate of Change46 sec

3.1.3. Example2 min

3.1.4. Practice1 min

3.2.1. The Limit Definition of a Derivative2 min

3.2.2. Example3 min

3.2.3. Practice5 min

3.2.4. When is Function Not Differentiable?

3.3.1. Differentiation Laws51 sec

3.4.1. The Power Rule1 min

3.4.2. Example2 min

3.4.3. Practice51 sec

3.5.1. Tangent Lines1 min

3.5.2. Example3 min

3.5.3. Practice2 min

3.6.1. Normal Lines1 min

3.6.2. Example3 min

3.6.3. Practice1 min

3.7.1. The Product Rule49 sec

3.7.2. Example2 min

3.7.3. Example2 min

3.7.4. Practice2 min

3.8.1. The Quotient Rule1 min

3.8.2. Example2 min

3.8.3. Practice4 min

3.9.1. The Chain Rule1 min

3.9.2. Example2 min

3.9.3. Practice3 min

3.10.1. Derivatives of Trigonometric Functions1 min

3.10.2. Example39 sec

3.10.3. Example3 min

3.10.4. Example1 min

3.10.5. Practice3 min

3.10.6. Practice2 min

3.11.1. Derivatives of Exponential Functions1 min

3.11.2. Example52 sec

3.11.3. Example3 min

3.11.4. Practice1 min

3.12.1. Higher Order Derivatives2 min

3.12.2. Example3 min

3.12.3. Practice2 min

3.12.4. Practice2 min

3.13.1. Implicit Differentiation2 min

3.13.2. Example3 min

3.13.3. Example3 min

3.13.4. Practice3 min

3.14.1. Derivatives of Inverse Functions52 sec

3.14.2. Example2 min

3.14.3. Practice3 min

3.15.1. Derivatives of Logarithmic Functions1 min

3.15.2. Example56 sec

3.15.3. Example2 min

3.15.4. Practice2 min

3.15.5. Practice: Log and Ln2 min

3.16.1. Inverse Trig Derivatives1 min

3.16.2. Example1 min

3.16.3. Practice3 min

3.17.1. Logarithmic Differentiation2 min

3.17.2. Example2 min

3.17.3. Practice3 min

3.18.1. Hyperbolic Functions and their Derivatives2 min

3.18.2. Example51 sec

3.18.3. Practice59 sec

3.19.1. Inverse Hyperbolic Functions and their Derivatives37 sec

3.19.2. Practice

4. Applications of Differentiation

4hr

4.1.1. Related Rates1 min

4.2.1. Differentials2 min

4.2.2. Example3 min

4.2.3. Practice2 min

4.3.1. Linearization (Linear Approximation)59 sec

4.3.2. Example3 min

4.3.3. Practice3 min

4.3.4. Practice3 min

4.4.1. Taylor Polynomials 1 min

4.4.2. Example6 min

4.4.3. Example4 min

4.4.4. Practice

4.5.1. Taylor Polynomial Remainder2 min

4.5.2. Example3 min

4.5.3. Practice

4.6.1. Newton's Method1 min

4.7.1. L’Hopital’s Rule2 min

4.7.2. Example2 min

4.7.3. Practice5 min

4.8.1. Solving General Indeterminate Forms2 min

4.8.2. Example2 min

4.8.3. Practice5 min

4.8.4. Practice2 min

4.9.1. Extreme Value Theorem1 min

4.10.1. Rolle's Theorem1 min

4.10.2. Example2 min

4.10.3. Practice1 min

4.11.1. Fermat's Theorem47 sec

4.12.1. The Mean Value Theorem1 min

4.12.2. Example2 min

4.12.3. Practice2 min

4.13.1. Intervals of Increase and Decrease1 min

4.13.2. Example2 min

4.13.3. Practice3 min

4.14.1. Critical Points and Extrema2 min

4.14.2. Example

4.14.3. Practice3 min

4.15.1. 1st and 2nd Derivative Tests3 min

4.15.2. Example7 min

4.15.3. Example

4.15.4. Practice3 min

4.16.1. Maximum and Minimum on Closed Intervals2 min

4.16.2. Example4 min

4.16.3. Practice3 min

4.16.4. Practice3 min

4.17.1. Concavity and Inflection Points56 sec

4.17.2. Example6 min

4.17.3. Practice6 min

4.18.1. Curve Sketching2 min

4.18.2. Example7 min

4.18.3. Practice9 min

4.18.4. Practice

4.19.1. Optimization1 min

4.19.2. Example4 min

4.19.3. Example4 min

4.19.4. Practice6 min

4.19.5. Practice4 min

4.20.1. Related Rates

4.20.2. Related Rates5 min

4.20.3. Related Rates5 min

4.20.4. Linear Approximation4 min

4.20.5. Linear Approximation

4.20.6. Taylor Series from Definition7 min

4.20.7. Taylor Polynomials

4.20.8. Maclaurin Polynomial

4.20.9. Newton's Method2 min

4.20.10. Newton's Method

4.20.11. L'Hopital's Rule

4.20.12. L'Hopital's Rule

4.20.13. L'Hopital's Rule

4.20.14. Limits

4.20.15. L'Hopital's Rule

4.20.16. L'Hopital's Rule

4.20.17. Limits

4.20.18. Limits

4.20.19. Extreme Value Theorem

4.20.20. Rolle's Theorem1 min

4.20.21. Rolle's Theorem6 min

4.20.26. Intervals of Increase and Decrease

4.20.27. Intervals of Increase and Decrease3 min

4.20.28. Critical Points6 min

4.20.29. Critical Points1 min

4.20.30. Extrema5 min

4.20.31. Extrema6 min

4.20.32. Second Derivative Test10 min

4.20.33. Curve Sketching

4.20.34. Curve Sketching12 min

4.20.35. Curve Sketching

4.20.36. Optimization

4.20.37. Optimization

4.20.38. Optimization

5. Applications of Differentiation for Science

41min

5.1.1. Position, Velocity, and Acceleration1 min

5.1.2. Example3 min

5.1.3. Practice2 min

5.2.1. Exponential Growth and Decay3 min

5.2.2. Example4 min

5.2.3. Example5 min

5.2.4. Practice5 min

5.3.1. Newton’s Law of Cooling1 min

5.3.2. Example5 min

5.3.3. Practice2 min

5.4.1. Velocity and Acceleration

5.4.2. Displacement, Velocity, & Acceleration9 min

5.4.3. Velocity and Acceleration

5.4.4. Exponential growth and decay

5.4.5. Exponential growth and decay

5.4.6. Exponential growth and decay

5.4.7. Exponential growth and decay

5.4.8. Newton's Law of heating and cooling

6. Integrals

2.7hr

6.1.1. Antiderivatives (Indefinite Integral)3 min

6.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

6.2.2. Example1 min

6.2.3. Practice1 min

6.2.4. Practice1 min

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

6.3.2. Example1 min

6.3.3. Practice1 min

6.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

6.4.2. Example42 sec

6.4.3. Practice1 min

6.4.4. Practice2 min

6.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

6.5.2. Example2 min

6.5.3. Practice1 min

6.6.1. Initial Conditions2 min

6.6.2. Example2 min

6.6.3. Practice5 min

6.7.1. Finite Sums & Summation Notation3 min

6.7.2. Example5 min

6.7.3. Practice4 min

6.7.4. Practice4 min

6.8.1. Approximating Areas & Riemann Sums 3 min

6.8.2. Example4 min

6.8.3. Practice3 min

6.9.1. The Definite Integrals & Area Under a Curve2 min

6.9.2. Example7 min

6.9.3. Practice2 min

6.9.4. Practice12 min

6.10.1. Properties of the Definite Integral2 min

6.10.2. Practice2 min

6.10.3. Practice2 min

6.11.1. Computing Definite Integrals Geometrically44 sec

6.11.2. Example1 min

6.11.3. Practice1 min

6.12.1. Fundamental Theorem of Calculus - Part I2 min

6.12.2. Example1 min

6.12.3. Example48 sec

6.12.4. Practice1 min

6.12.5. Practice2 min

6.13.1. Fundamental Theorem of Calculus - Part 21 min

6.13.2. Example2 min

6.13.3. Example

6.13.4. Practice 4 min

6.13.5. Practice3 min

6.13.6. Practice1 min

6.14.1. Integration by Substitution2 min

6.14.2. Example4 min

6.14.3. Example3 min

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

6.14.5. Practice

6.14.6. Practice

6.14.7. Practice

6.14.8. Practice (w/ Back-Substitution)

7. Applications of Integration

1.8hr

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

7.1.2. Example6 min

7.1.3. Practice

7.1.4. Practice

7.2.1. Average Value of a Function47 sec

7.2.2. Example2 min

7.2.3. Practice2 min

7.3.1. Area between curves1 min

7.3.2. Example5 min

7.3.3. Example5 min

7.3.4. Practice

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

7.5.1. Volumes of Revolution by Cylindrical Shells2 min

7.5.2. Practice

7.5.3. Practice

7.6.1. Arc Length41 sec

7.6.2. Example3 min

7.6.3. Practice4 min

7.7.1. Surface Area of Revolution1 min

7.7.2. Example5 min

7.7.3. Practice

8. Applications of Integration for Physical Science

60min

9. Integration Techniques

2.4hr

9.1.1. Integrating Even and Odd Functions2 min

9.1.2. Example2 min

9.1.3. Practice2 min

9.2.1. Integration by Parts3 min

9.3.1. Trigonometric Integrals5 min

9.3.2. Example3 min

9.3.3. Example: Trigonometric Integrals (Case 1-3)3 min

9.4.1. Trigonometric Substitution3 min

9.4.2. Example7 min

9.4.3. Practice

9.4.4. Practice

9.5.1. Partial Fractions Decomposition4 min

9.6.1. The Midpoint Rule1 min

9.6.2. Example2 min

9.7.1. The Trapezoid Rule 1 min

9.7.2. Example2 min

9.7.3. Practice

9.8.1. Simpson's Rule1 min

9.8.2. Example2 min

9.8.3. Practice

9.9.1. Error Bounds for Approximations2 min

9.9.2. Practice

9.10.1. Integration by Parts2 min

9.10.2. Integration by Parts

9.10.3. Integration by Parts

9.10.4. Integration by Parts

9.10.5. Integration by Parts

9.10.6. Trigonometric Integral3 min

9.10.7. Trigonometric Integral

9.10.8. Trigonometric Integral with IBP5 min

9.10.9. Trigonometric Substitution5 min

9.10.10. Trigonometric Substitution6 min

9.10.11. Trigonometric Substitution8 min

9.10.12. Partial Fraction Decomposition8 min

9.10.13. Partial Fraction Decomposition24 min

9.10.14. Partial Fraction Decomposition4 min

9.10.15. The Trapezoid Rule

9.10.16. The Trapezoid Rule2 min

9.10.17. Simpson's Rule

10. Differential Equations

1.2hr

10.1.1. Differential Equations8 min

10.1.2. Direction Fields/Slope Fields5 min

10.1.3. Practice Question: DE Solution Graphs3 min

10.2.1. Separable First Order Differential Equations3 min

10.2.2. Practice (separable DE)2 min

10.2.3. Practice (IVP)3 min

10.2.4. Practice (IVP)3 min

10.2.5. Practice (IVP*)5 min

10.2.6. Practice (separable DE)1 min

10.3.1. Linear First Order Differential Equations7 min

10.3.2. Practice (integrating factor)1 min

10.3.3. Practice (linear DE)3 min

10.3.4. Practice (IVP)3 min

10.3.5. Practice (IVP)4 min

10.4.1. Exponential Growth and Decay3 min

10.4.2. Example4 min

10.4.3. Example5 min

10.4.4. Practice5 min

10.4.5. Practice (population)3 min

10.4.6. Practice (population)4 min

10.5.1. Second-Order Reducible DE

10.5.2. Practice: Dependent Variable Missing

10.5.3. Practice: Independent Variable Missing

10.Q. DE Quiz4 Qns

MATH 1225A/B

Course Overview

1. Pre-Calculus (Review)

2. Limits

3. Derivatives

4. Applications of Differentiation

5. Applications of Differentiation for Science

6. Integrals

7. Applications of Integration

8. Applications of Integration for Physical Science

9. Integration Techniques

10. Differential Equations

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