#### Calculus

### Course Description

### Limits and continuity

Limits intro

Estimating limit from graphs

Estimating limit from table

Formal definition of limits

Properties of limits

Limits by direct substitution

Limits using algebraic manipulation

strategy in finding limits

Squeeze theorem

Types of discontinuities

continuity at a point

Continuity over an interval

Removing discontinuities

### Derivatives: definition and basic rules

Average vs instantaneous rate of change

secant lines

Derivation Definition

Estimating Derivative

Differentiability

Power rule

Derivative rule : constant ,sum, difference and constant rule

Combining the power rule with other derivative rule

Derivative of cos(X),sin(X),In(x)

product rule

quotient rule

Derivation of tan(X),cot(x),sec(x), cos(x)

Proof video

### Derivatives: chain rule and other advanced topics

Chain rule

more chain rule

Implicit differentiation

Implicit differentiation (advance example)\

Differentiating inverse function

Derivate of inverse trigonometric function \

strategy in different function

differentiations using multiple rule

second derivations

Disguised derivatives

Logarithmic differentiation

second derivative

Disguised derivatives

Logarithmic differentiation

proof video

### Applications of derivatives

Meaning of the derivatives in context

Straight in line motion

Non-motion application of derivatives

introduction to related rates

Solving related rates problems

Approximation with local linearity

L ‘Hospital’s rule

L” Hospital :composite exponential functions

### Analyzing functions

Mean value theorem

Extreme value theorem and critical points

Interval on which a function is increasing or decreasing

Relative (local) extreme

Absolute (global)extreme

Concavity and inflection points intro

Analyzing concavity and inflection points

Second derivatives test

Sketching curve

Connecting f, “f” and f”

solving optimization problems

Analyzing implicit relation

Calculator-active practice

### Integrals

Accumulations of change introduction

Approximation with Riemann sums

Summations notations review

Riemann sums is summations notations

Defining integrals with Riemann sums

Fundamental theorem of calculus and accmulation functions

Interpreting the behavior of accumulations functions

Properties of definite integrals

Fundamental theorem of calculus and definite integrals

Reverse power rule

Indefinite integral of common function

Definite integral of common function

Integrating with u-substitution

Integral using long division and completing the square

Integrating using trigonometric identities

Proof videos

Differential equations

Differential equations Introduction

Verifying solution for different equations

Sketching solve field

Reasoning using slope field

Particular solutions to different equations

Exponential models

Applications of integrals

Average value of a function

Straight-line motion

Non -motion application of integral

Area: vertical area between curve

Area: horizontal area between curve

Area: curve that intersect more than between two points

Volume : Square and rectangles cross sections

Volume: triangle and semicircle cross section

Volume : disc method (revolving around x-and y-axes)

Volume : disc method (revolving around other axes)

volume: washer method (revolving around x-and y-axes)

volume: washer method (revolving around other axes)

calculator active practice.

### COURCE CHALLENGE

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.

There are no reviews yet.