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MTH 251/252/253 – Calculus

MTH 251/252/253 – Calculus. Full Year Review. MTH251 – Differential Calculus. Limits Continuity Derivatives Applications. MTH251 – Differential Calculus. Limits Evaluate limits at a point. Evaluate end behavior limits. Evaluate limits of quotients. L’Hôpitals Rule.

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MTH 251/252/253 – Calculus

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  1. MTH 251/252/253 – Calculus Full Year Review

  2. MTH251 – Differential Calculus • Limits • Continuity • Derivatives • Applications

  3. MTH251 – Differential Calculus • Limits • Evaluate limits at a point. • Evaluate end behavior limits. • Evaluate limits of quotients. • L’Hôpitals Rule

  4. MTH251 – Differential Calculus • Continuity • Where does discontinuity occur? • Jumps (piecewise functions) • Asymptotes • Holes • Intervals where the function is undefined • Given a graph or equation of a function; indicate where the function is discontinuous

  5. MTH251 – Differential Calculus • Derivatives • Polynomials • Trigonometric and Inverse Trigonometric • Exponential • Logarithmic (esp. Natural Logs) • Products • Quotients • Chain Rule

  6. MTH251 – Differential Calculus • Applications • Optimization Problems (i.e. max/min problems) • Equations of tangent lines • Rectangular • Parametric

  7. MTH252 – Integral Calculus • Indefinite Integrals • Definite Integrals • Methods of Integration • Applications

  8. MTH252 – Integral Calculus • Indefinite Integrals • Antiderivative F(x) is an antiderivative of f(x) iff F’(x) = f(x) • Indefinite Integral The set of all antiderivatives of a function.

  9. MTH252 – Integral Calculus • Definite Integrals • The limit of a Riemann Sum • The Fundamental Theorem of Calculus

  10. MTH252 – Integral Calculus • Methods of Integration • Recognition: poly, trig, exp, log, … • Algebraic Manipulation • (Simple) Substitution • Parts • Powers of Trigonometric Functions • Trigonometric Substitutions • Partial Fractions

  11. MTH252 – Integral Calculus • Applications • Area Problems

  12. MTH253 – Analytic Geometry, Sequences, & Series • Conics • Polar Coordinates & Equations • Sequences • Series w/ Tests for Convergence • Taylor & Maclaurin Series

  13. MTH253 – Analytic Geometry, Sequences, & Series • Conics • Rotate (eliminate Bxy) • Translate (eliminate Dx and Ey) … complete the squares • Parabola • Ellipse • Circle • Hyperbola • Polar Forms Foci: Eccentricity: Directrixes:

  14. MTH253 – Analytic Geometry, Sequences, & Series • Polar Coordinates & Equations • Locate & Identify Points • Graph Equations • Circles, Flowers, Limaçons/Cardiods, Leminiscates, & Spirals • Convert to and from Rectangular Coordinates & Equations • Tangent Lines

  15. MTH253 – Analytic Geometry, Sequences, & Series • Sequences • An Ordered Set or List of Numbers • Notation • Given the first several terms, find the nth term. • Evens  2n • Odds  2n+1 or 2n-1 • Alternating  (–1)nor (–1)n+1 • Constant Increment  kn + a • Factorials  n! or (n + a)! or (n – a)! • Convergence

  16. MTH253 – Analytic Geometry, Sequences, & Series • Series • The sum of the terms of a sequence. • Notation • Sequence of partial sums • Test for Convergence • Divergence Test • Geometric Series & P-Series • Integral • Comparison & Limit Comparison • Ratio & Root • Alternating Series and Absolute Convergence

  17. MTH253 – Analytic Geometry, Sequences, & Series • Taylor & Maclaurin Series • Taylor Series at x = a • Maclaurin Series • Three Important Maclaurin Series

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