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حساب التفاضل
Chapter1: Functions
1.1Sets of Numbers and Inequalities
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1.1Sets of Numbers and Inequalities
Set definition: union, intersection, belong, subset.
Set of numbers – real (number) line
Set of numbers: Exercise
Intervals
Inequalities – linear inequality
Rational inequality
Rational Inequality Exercise – Part 1
Rational Inequality Exercise – Part 2
quadratic inequality exercise
absolute functions – absolute inequality
1.2Functions
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1.2Functions
constants – Variables – function defination – vertical line test
Domain and range exercises Part (1)
Domain and range exercises Part (2)
Two function equality
Combining Functions (algebra of functions)
intercepts
Symmetry – even and odd functions
Value of a function
Function Composition
1.3Inverse Functions
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1.3Inverse Functions
one-to-one functions
Inverse functions
1.4Trigonometric Functions and Their Inverses
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1.4Trigonometric Functions and Their Inverses
Angle – angle measure (degree , radian)
Trigonometric functions
Trigonometric functions with two familiar triangles
Reference angle and Phythagorous – Relations
sign of trigonometric functions
Trigonometric identity
Graphs of Trigonometric functions
inverse of sine and cosine functions – tan and cotan – sec and csc
Chapter2: Limits and Continuity
2.1Definition of Limit
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2.1Definition of Limit
Tabular and graphical methods
examples on tabular and graphical methods
formal definition (epsilon-delta method)
one-sided limit
examples on one-sided limits part 1
examples on one-sided limits part 2
one-sidedformal definition (epsilon-delta method)
2.2Limits Laws
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2.2Limits Laws
algebra of limits part 1
algebra of limits part 2
algebra of limits part 3
squeeze (sandwich) theorem
Trigonometric functions limits
2.3Limits Involving Infinity
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2.3Limits Involving Infinity
infinite limits
vertical asymptote
limits at infinty
horizontal asymptote
2.4Continuity of Functions
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2.4Continuity of Functions
Continuity at a point and Continuous Functions part 1
Continuity at a point and Continuous Functions part 2
Continuity at a point and Continuous Functions part 3
continuity of composite functions
Intermediate value theorem
Chapter3: Continuity Of Functions
3.1The Derivative and Tangent Line Problem
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3.1The Derivative and Tangent Line Problem
DERIVATIVE AND THE TANGENT
Examples part 1
Examples part 2
Examples part 3
Differentiability
3.2Differentiation Rules
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3.2Differentiation Rules
DIFFERENTIATION RULES
Examples
DIFFERENTIATION RULES (Continued)
3.3Derivatives Of Trigonometric Functions
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3.3Derivatives Of Trigonometric Functions
DERIVATIVE OF TRIGONOMETRIC FUNCTION
3.4The Chain Rule
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3.4The Chain Rule
Chain Rule (General Power Rule)
Chain Rule (General Trigonometric Functions)
3.5Implicit Differentiation
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3.5Implicit Differentiation
IMPLICIT DIFFERENTIATION
3.6Higher Order Derivatives
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3.6Higher Order Derivatives
HIGHER ORDER DERIVATIVES
Examples
3.7The Derivative Of Inverse Functions
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3.7The Derivative Of Inverse Functions
Derivative of Inverse Trigonometric Functions
Chapter4: Applications Of Differentiation
4.1Extrema Of Functions
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4.1Extrema Of Functions
Absolute extrema
Critical points
Find absolute extrema on close interval using critical points
4.2The Mean Value Theorem
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4.2The Mean Value Theorem
Rolle’s Theorem
“Mean Value Theorem (Lagrange’s Theorem)”
4.3Increasing and Decreasing Functions
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4.3Increasing and Decreasing Functions
Increasing and Decreasing Functions – Monotonic Functions
Increasing and decreasing test
“First derivative test (Finding Local Extrema)”
4.4Concavity
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4.4Concavity
“Second derivative test (Finding Concavity)”
Point of Inflection
“Second derivative test (Finding Local Extrema)”
4.5Curve Sketching
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4.5Curve Sketching
Curve-Sketching -Exercise part 1
Curve-Sketching -Exercise part 2
Curve-Sketching -Exercise part 3
Slant Asymptote
1 من 2
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1.3Inverse Functions
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1.3Inverse Functions
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one-to-one functions
Inverse functions
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