1. Discrete Dynamical Systems

14min

1.1.1. Discrete Time Dynamical Systems2 min

1.1.2. The updating function, Part I1 min

1.1.3. The Updating Function, Part II3 min

1.1.4. The Updating Function, Part III2 min

1.1.5. Example: Dynamical System 12 min

1.1.6. Example: Dynamical System 247 sec

1.1.7. Example: Dynamical System 32 min

1.1.8. Example: Dynamical System 452 sec

1.2.1. Equilibria

1.2.2. Cobwebbing

1.2.3. Example: Cobwebbing for Linear Function

1.2.4. Practice: Drug Concentration, Linear

1.2.5. Practice: At Equilibrium

1.2.6. Example: Parabola with Spiral

1.2.7. Practice: Spiral Cobweb

1.2.8. Practice: Parabola

1.Q. Checkpoint Quiz (Coming soon!)5 Qns

2. Rates of change, Limits, Trig. Functions

1.4hr

2.1.1. Average Rate of Change & the Secant Line2 min

2.1.2. Example

2.1.3. Practice Level 12 min

2.1.4. Practice Level 2

2.1.5. Practice Level 3

2.2.1. Instantaneous Rate of Change & the Tangent Line4 min

2.2.2. Example2 min

2.2.3. Practice Level 1

2.2.4. Practice Level 2

2.2.5. Practice Level 3

2.3.1. Limit Basics2 min

2.3.2. Example1 min

2.4.1. One-Sided Limits2 min

2.4.2. Example: One-Sided Limit2 min

2.4.3. Practice: One-Sided Limits3 min

2.5.1. Limit Laws 2 min

2.5.2. Practice1 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. The Squeeze Theorem2 min

2.9.2. Example2 min

2.9.3. Practice2 min

2.10.1. Infinite Limits2 min

2.10.2. Example1 min

2.10.3. Example3 min

2.11.1. Limits at Infinity3 min

2.11.2. Example60 sec

2.11.3. Example3 min

2.11.4. Example4 min

2.11.5. Practice 3 min

2.11.6. Practice3 min

2.12.1. Trigonometric Functions6 min

2.12.2. Example4 min

2.12.3. Trig Identities2 min

2.12.4. Practice3 min

2.12.5. Practice4 min

3. Continuity, Differentiation, Exponential Functions

35min

3.1.1. Continuity2 min

3.1.2. Example2 min

3.1.3. Practice4 min

3.2.1. Derivatives as a Rate of Change2 min

3.2.2. Average Rate of Change46 sec

3.2.3. Example2 min

3.2.4. Practice1 min

3.3.1. The Limit Definition of a Derivative2 min

3.3.2. Example3 min

3.3.3. Practice5 min

3.4.1. Differentiation Laws51 sec

3.5.1. The Power Rule1 min

3.5.2. Example2 min

3.5.3. Practice51 sec

3.6.1. Exponential Functions3 min

3.6.2. Example1 min

3.6.3. Example2 min

4. More derivatives, Implicit derivatives, Logarithmic Functions

58min

4.1.1. The Product Rule49 sec

4.1.2. Example2 min

4.1.3. Example2 min

4.1.4. Practice2 min

4.2.1. The Quotient Rule1 min

4.2.2. Example2 min

4.2.3. Practice4 min

4.3.1. The Chain Rule1 min

4.3.2. Example2 min

4.3.3. Practice3 min

4.4.1. Logarithmic Functions4 min

4.4.2. Example3 min

4.4.3. Example:3 min

4.4.4. Practice2 min

4.5.1. Derivatives of Logarithmic Functions1 min

4.5.2. Example56 sec

4.5.3. Example2 min

4.5.4. Practice2 min

4.5.5. Practice: Log and Ln2 min

4.6.1. Implicit Differentiation2 min

4.6.2. Example3 min

4.6.3. Example3 min

4.6.4. Practice3 min

4.7.1. Logarithmic Differentiation2 min

4.7.2. Example2 min

4.7.3. Practice3 min

5. Trig. Derivatives, Related Rates, Second Derivatives, Linear Approximation

55min

6. Max/Min, Graphing

1.2hr

7. L'Hôpital's rule, Taylor Polynomials

20min

7.1.1. L’Hopital’s Rule2 min

7.1.2. Example2 min

7.1.3. Practice5 min

7.2.1. Taylor Polynomials 1 min

7.2.2. Example6 min

7.2.3. Example4 min

7.2.4. Practice

8. Equilibria & derivatives, Logistic Equation, Differential Equations

23min

8.1.1. Logistic Equation4 min

8.1.2. Example: Logistic Equation43 sec

8.1.3. Example5 min

8.2.1. Types of Differential Equations

8.2.2. Example

8.2.3. Types of Differential Equations

8.3.1. Theory: Separable Differential Equations2 min

8.3.2. Example: Solving a Separable Differential Equation6 min

8.3.3. Practice

8.4.1. Definition of a Linear Differential Equation2 min

8.4.2. Solution of y' = ay3 min

8.5.1. Initial Value Problem

8.5.2. Initial Value Problem

8.5.3. Practice

8.5.4. Practice

9. Euler's Method, Antiderivatives, Definite Integrals, Riemann Sums

1.4hr

9.I. Chapter Intro18 sec

9.1.1. Example

9.1.2. Example

9.1.3. Example

9.2.1. Antiderivatives (Indefinite Integral)3 min

9.3.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

9.3.2. Example2 min

9.3.3. Practice1 min

9.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

9.4.2. Example42 sec

9.4.3. Practice1 min

9.4.4. Practice2 min

9.5.1. Computing Definite Integrals Geometrically44 sec

9.5.2. Example1 min

9.5.3. Practice1 min

9.6.1. Finite Sums & Summation Notation3 min

9.6.2. Example5 min

9.6.3. Practice4 min

9.6.4. Practice4 min

9.7.1. Approximating Areas & Riemann Sums 3 min

9.7.2. Example4 min

9.7.3. Practice3 min

9.8.1. The Definite Integrals & Area Under a Curve2 min

9.8.2. Example7 min

9.8.3. Practice2 min

9.8.4. Practice12 min

9.9.1. Properties of the Definite Integral2 min

9.9.2. Practice2 min

9.9.3. Practice2 min

9.10.1. Initial Conditions2 min

9.10.2. Example2 min

9.10.3. Practice5 min

10. FTOC, Substitution, Autonomous Differential Equations

1.2hr

10.1.1. Fundamental Theorem of Calculus - Part I2 min

10.1.2. Example1 min

10.1.3. Example48 sec

10.1.4. Practice1 min

10.1.5. Practice2 min

10.2.1. Fundamental Theorem of Calculus - Part 21 min

10.2.2. Example2 min

10.2.3. Example

10.2.4. Practice 4 min

10.2.5. Practice3 min

10.2.6. Practice1 min

10.3.1. Integration by Substitution2 min

10.3.2. Example4 min

10.3.3. Example3 min

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

10.3.5. Practice

10.3.6. Practice

10.3.7. Practice

10.3.8. Practice (w/ Back-Substitution)

10.4.1. Pure-Time Differential Equations4 min

10.4.2. Initial Conditions2 min

10.4.3. Example: Position from Velocity3 min

10.4.4. Practice:

f

from

f''

4 min

10.4.5. Practice: Position from Acceleration3 min

10.4.6. Practice: Rearrange First3 min

10.4.7. Autonomous Differential Equations48 sec

10.4.8. Example: Autonomous Differential Equation1 min

10.4.9. Practice: Autonomous Differential Equations43 sec

10.5.1. Equilibria2 min

10.5.2. Phase Plots4 min

10.5.3. Example: Phase Plot for Given Graph2 min

10.5.4. Practice: Phase Plot for Given Graph1 min

10.5.5. Example: Equilibria and Stability2 min

10.5.6. Practice: Equilibria and Stability3 min

10.5.7. Practice: Find Equilibria with Given Constants2 min

11. Integration by Parts, Separable Differential Equations, Systems of Differential Equations

26min

11.1.1. Integration by Parts8 min

11.1.2. Example: Repeated Integration by Parts4 min

11.1.3. Example: Integration by Parts Special Case5 min

11.1.4. Example: Integration by Parts with the Natural Logarithm2 min

11.2.1. Separable First Order Differential Equations1 min

11.2.2. Separable Differential Equations

11.2.3. Example: Solving a Separable Differential Equation6 min

MATH 1215

Course Overview

1. Discrete Dynamical Systems

2. Rates of change, Limits, Trig. Functions

3. Continuity, Differentiation, Exponential Functions

4. More derivatives, Implicit derivatives, Logarithmic Functions

5. Trig. Derivatives, Related Rates, Second Derivatives, Linear Approximation

6. Max/Min, Graphing

7. L'Hôpital's rule, Taylor Polynomials

8. Equilibria & derivatives, Logistic Equation, Differential Equations

9. Euler's Method, Antiderivatives, Definite Integrals, Riemann Sums

10. FTOC, Substitution, Autonomous Differential Equations

11. Integration by Parts, Separable Differential Equations, Systems of Differential Equations

12. Integration by Taylor Polynomials

Midterm test Overview

Course Notes