BMA Calculus Videos

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  • Chapter 1:
  • Review of Functions (YouTube Link)
    Review of Exponential Functions (YouTube Link)
    Review of Shifting & Translating Functions (YouTube Link)
    Log Rules, a review of logarithms and their rules (YouTube Link)
    Very quick review of trigonometry (YouTube Link)

  • Chapter 2:
  • A: Finding the slope of a curved line. (YouTube Link)
    B: Definition of the derivative. (YouTube Link)
    C: Developing the power rule for taking derivatives. (YouTube Link)
    D: Example of taking the derivative of 1/x. (YouTube Link)
    E: Example showing how to take the derivative of sin(x). (YouTube Link)
    F: Example showing how to take derivatives of e^x and a^x. (YouTube Link)
    G: Comparing graphs of functions and their derivatives. (YouTube Link)
    H: Graphing the 2nd derivative with the 1st derivative & f(x). (YouTube Link)
    I: Use a graph of f(x) to construct a graph of the derivative f'(x) (YouTube Link)
    J: Using a graph of f'(x) to construct a graph of f(x). (YouTube Link)
    K: The price of Oreos to generate a graph of the derivative. (YouTube Link)
    L: A graph of the derivative in order to generate a graph of f(x). (YouTube Link)

  • Chapter 3:
  • A: Derivative Rules: Constant Multiple, Addition, Subtraction. (YouTube Link)
    B: Derivative Rules: The power rule. (YouTube Link)
    C: What is e, beyond 2.71828..., the exponential number. (YouTube Link)
    D: Derivatives rules: exponential functions. (YouTube Link)
    E: Derivative Rules: The chain rule. (YouTube Link)
    F: Derivative Rules: trigonometric functions. (YouTube Link)
    G: Derivative Rules: Trigonometric Functions. (YouTube Link)
    H: Derivative Rules: The Product Rule. (YouTube Link)
    I: Derivative Rules: The quotient rule. (YouTube Link)
    J: Derivative Rules: The tangent function. (YouTube Link)
    K: Derivative Rules: Implicit Differentiation. (YouTube Link)
    L: Derivative Rules: Inverse Functions. (YouTube Link)
    M: Derivative Rules: All of them very fast. (YouTube Link)
    N: Chain Rule fast method. (YouTube Link)
    O: Product Rule very fast. (YouTube Link)
    P: Deriving the Power Rule, Binomial Theorem (YouTube Link)

  • Chapter 4:
  • A: Using Calculus to Find the Vertex of a Parabola. (YouTube Link)
    B: Max, min and point of inflection of a cubic equation. (YouTube Link)
    C: 1st & 2nd derivatives to find max, min & point of inflection. (YouTube Link)
    D: Calculus on equations of motion with constant acceleration. (YouTube Link)
    E: Applying Calculus to the Normal Distribution. (YouTube Link)
    F: Business Calculus, how to make money knitting sweaters. (YouTube Link)
    G: Using calculus to find ideal dimensions of a can. (YouTube Link)
    H: Using Calculus to find the quickest path in Orienteering. (YouTube Link)
    I: Using Calculus on the Doppler Effect and the Cosine Effect. (YouTube Link)
    J: Related Rates, how fast does a cone of gravel grow over time (YouTube Link)
    K: Using Calculus on a moving shadow under a streetlight. (YouTube Link)

  • Chapter 5:
  • A: Introduction to Integration and the Integral. (YouTube Link)
    B: Riemann Sums, Area under a curve, intro to the integral. (YouTube Link)
    C: Riemann Sums and motion with constant acceleration. (YouTube Link)
    D: Fundamental Theorem of Calculus, Area under the curve. (YouTube Link)
    E: Distance traveled by a ball accelerating to terminal velocity. (YouTube Link)
    F: Preview of tricks and rules of integration. (YouTube Link)
    G: Area under a curve manually with paper and scissors. (YouTube Link)
    H: Using Integration to find the average value of a function. (YouTube Link)
    I: Symmetry in integrals, negative area, odd & even functions. (YouTube Link)
    J: A closer look at definite integration. (YouTube Link)

  • Chapter 6:
  • A: Integrals, Anti-derivatives, Area under curves. (YouTube Link)
    B: Slope fields used to construct anti-derivatives. (YouTube Link)
    C: Slope fields and anti-derivatives continued. (YouTube Link)
    D: Finding integrals with spreadsheets, Riemann Sums. (YouTube Link)
    E: Riemann Sums, area under the curve, continued. (YouTube Link)
    F: Power Rule for finding anti-derivatives. (YouTube Link)
    G: Integrals found from memorized derivatives. (YouTube Link)
    H: Super Basic Differential Equation Example. (YouTube Link)
    I: A note about +C in the integral. (YouTube Link)
    J: A look at internet-based Integral Calculators. (YouTube Link)
    K: Notes about limits of integration, definite integrals. (YouTube Link)

  • Chapter 7:
  • A: Introduction to Integration By Substitution (YouTube Link)
    B: Integration by Substitution Worked Examples (YouTube Link)
    C: Common Mistake in Integration by Substitution (YouTube Link)
    D: Advanced example of Integration by Substitution (YouTube Link)
    E: Introduction to Integration by Parts (YouTube Link)
    F: Integration by Parts worked examples (YouTube Link)
    G: Integration by Parts "circular" example (YouTube Link)
    H: Intro to Integration by Partial Fractions (YouTube Link)
    I: Integration by Partial Fractions Examples (YouTube Link)
    J: More Integration by Partial Fractions rules. (YouTube Link)
    K: Intro to Integration by Trigonometric Substitution (YouTube Link)
    L: Integration by Trigonometric Substitution Examples (YouTube Link)
    M: Advanced Integration by Trig Substitution (YouTube Link)
    N: Intro to Improper Integrals (YouTube Link)
    O: Online, Web-based Integral Calculators (YouTube Link)
    P: Improper Integrals, Singularities Hidden In Limits. (YouTube Link)

  • Chapter 8:
  • A: Finding the area enclosed by two curves (YouTube Link)
    B: Using integration to derive the volume of a sphere (YouTube Link)
    C: Using integration to derive the volume of an ellipsoid (YouTube Link)
    D: Advanced: deriving the area of an ellipse (YouTube Link)
    E: Calculating the length of a curve (YouTube Link)
    F: Calculating the surface area of a revolved function (YouTube Link)
    G: Disk Method, volume of a revolved function f(x) around x (YouTube Link)
    H: Shell Method, volume of a revolved function f(x) around y (YouTube Link)
    I: Converting between rectangular and polar coordinates (YouTube Link)
    J: Area in polar coordinates (YouTube Link)
    K: Curve length in polar coordinates (YouTube Link)

  • Chapter 11:
  • A: Overview of Differential Equations and their solutions (YouTube Link)
    B: Slope Fields applied to Differential Equations (YouTube Link)
    C: Computer Generated Slope Fields (YouTube Link)
    D: Euler's Method of solving Diff. Eq.'s using a spreadsheet (YouTube Link)
    E: Separable Differential Equations (YouTube Link)
    F: A note on domain and range in Differential Equations (YouTube Link)
    G: First Order Linear Differential Equations (YouTube Link)
    H: Second Order Homogeneous Linear Differential Equations (YouTube Link)
    I: 2nd Order Non-Homogeneous Linear Differential Equations (YouTube Link)