Download presentation

Presentation is loading. Please wait.

Published byLaureen Copeland Modified over 3 years ago

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

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

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

15
Sequences An Ordered Set or List of Numbers Notation Given the first several terms, find the n th term. Evens 2n Odds 2n+1 or 2n-1 Alternating (–1) n or (–1) n+1 Constant Increment kn + a Factorials n! or (n + a)! or (n – a)! Convergence MTH253 – Analytic Geometry, Sequences, & Series

16
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 MTH253 – Analytic Geometry, Sequences, & Series

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

Similar presentations

OK

Indefinite integrals Definition: if f(x) be any differentiable function of such that d/dx f( x ) = f(x)Is called an anti-derivative or an indefinite integral.

Indefinite integrals Definition: if f(x) be any differentiable function of such that d/dx f( x ) = f(x)Is called an anti-derivative or an indefinite integral.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google