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حساب التفاضل

عاصم ابراهيم

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حساب التفاضل

نظرة عامة على الدورة:
حساب التفاضل (من المفاهيم الأساسية إلى التطبيقات)

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من يرغب في تقوية مهاراته الرياضية.

الهدف العام للدورة:
تنمية قدرة المتعلم على التعامل مع الدوال والاشتقاق وتطبيقاته المختلفة في حل المشكلات الرياضية والعملية.

محتوى الدورة

Chapter1: Functions

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Set definition: union, intersection, belong, subset.

Set of numbers – real (number) line

Set of numbers: Exercise

Inequalities – linear inequality

Rational inequality

Rational Inequality Exercise – Part 1

Rational Inequality Exercise – Part 2

quadratic inequality exercise

absolute functions – absolute inequality

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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)

Symmetry – even and odd functions

Value of a function

Function Composition

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one-to-one functions

Inverse functions

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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

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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)

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algebra of limits part 1

algebra of limits part 2

algebra of limits part 3

squeeze (sandwich) theorem

Trigonometric functions limits

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infinite limits

vertical asymptote

limits at infinty

horizontal asymptote

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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

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DERIVATIVE AND THE TANGENT

Examples part 1

Examples part 2

Examples part 3

Differentiability

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DIFFERENTIATION RULES

DIFFERENTIATION RULES (Continued)

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DERIVATIVE OF TRIGONOMETRIC FUNCTION

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Chain Rule (General Power Rule)

Chain Rule (General Trigonometric Functions)

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IMPLICIT DIFFERENTIATION

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HIGHER ORDER DERIVATIVES

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Derivative of Inverse Trigonometric Functions

Chapter4: Applications Of Differentiation

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Absolute extrema

Critical points

Find absolute extrema on close interval using critical points

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Rolle’s Theorem

“Mean Value Theorem (Lagrange’s Theorem)”

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Increasing and Decreasing Functions – Monotonic Functions

Increasing and decreasing test

“First derivative test (Finding Local Extrema)”

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“Second derivative test (Finding Concavity)”

Point of Inflection

“Second derivative test (Finding Local Extrema)”

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Curve-Sketching -Exercise part 1

Curve-Sketching -Exercise part 2

Curve-Sketching -Exercise part 3

Slant Asymptote

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