MA 152

MA 152 - Calculus II

  1. Review
    a) Fundamental Theorem of Calculus, Definite Integral
    b) Area Under Curve, Substitution Method

  2. Applications of Integration
    a) Area between two curves
    b) Volume of a Solid of Revolution - Disk and Shell methods
    c) Arc length
    d) Area of a surface of revolution (optional)

  3. Techniques of Integration
    a) Inverse trigonometric functions and their derivatives
    b) Integration by parts
    c) Trigonometric integrals
    d Trigonometric substitutions
    e) Method of partial fractions
    f) Numerical integration (Trapezoidal Estimate, Simpson's Rule) (optional)

  4. Indeterminate Forms and Improper Integrals
    a) Indeterminate forms, L'Hopital's Rule
    b) Improper integrals

  5. Infinite Series
    a) Sequences
    b) Convergent and divergent series
    c) Integral test and p-series
    d) Direct Comparison and Limit Comparison Test
    e) Ratio and Root Test
    f) Power series - radius and interval of convergence
    g) Representing functions as power series
    h) Maclaurin and Taylor series

  6. Parametric Equations and Polar Coordinates
    a) Parametric equations
    b) Tangent lines and arc length
    c) Rectangular and polar coordinates
    d) Graphs of polar equations
    e) Area in polar coordinates

    Learning Outcome 1: The student will demonstrate an understanding of integration techniques.

    Learning Outcome 2: The student will demonstrate an understanding of calculus involving solids of revolution and the arc length of a curve.

    Learning Outcome 3: The student will understand the concept of infinite series.