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Differential CalculusBasic concepts of calculus such as limits, continuity and differentiability of functions;

differentiation of algebraic and transcendental functions involving one or more variables:

applications of differential calculus to problems on optimization, rates of change, related rates,tangents and normals, and approximations; partial differentiation and transcendental curve

tracing.

Number of Units for Lecture4 hours lecture

Number if Contact Hours per Week4 hours lecture

ObjectivesAfter completing this course, the student must be able to:

1. Have a working knowledge of the basic concepts of functions and limits;2.

Differentiate algebraic and transcendental functions with ease;3. Apply the concept of differentiation in solving word problems involving optimization, relatedrates, and approximation; and

4. Analyze and trace transcendental curves.C O U R S E O U T L I N E

1. Functions Naci John1.1 Definitions1.2 Classification of Functions1.3 Domain and Range of a Function1.4 Graph of a function1.5 Functional Notation1.6 Evaluation of a Function1.7 Combinations of Functions1.8 One-Valued and Many-Valued Functions1.9 Odd and Even Functions1.10 Special Function Types1.11 Functions as Mathematical Models

2. Continuity Naci John2.1 Definition2.2 Properties of Continuous Functions

3. Limits Naci John3.1 Notion of a Limit3.2 Definition3.3 Properties of Limits3.4 Operations with Limits3.5 Evaluation of Limits3.6 One-sided Limits3.7 Unbounded Functions

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4. The Derivative Naci John4.1 Notion of the Derivative4.2 Definition4.3 Determination of the Derivative by Increments4.4 Differentiation Rules

5. The Slope Naci John5.1 Definition of Slope as the Derivative of a Function5.2 Determination of the Slope of a Curve at a Given Point

6. Rate of Change Sharon Rose6.1 Average rate of Change6.2 Instantaneous Rate of Change

7. The Chain Rule and the General Power Rule Sharon Rose8. Implicit Differentiation Sharon Rose9. Higher-Order Derivatives Sharon Rose10.Polynomial Curves Naci John

10.1 Generalities About Straight Lines10.2 Tangents and Normal to Curves10.3 Extrema and the First Derivative Test10.4 Concavity and the Second Derivative Test10.5 Points of Inflection10.6 Sketching Polynomial Curves

11.Applications of the Derivative: Optimization Problems Sharon Rose12.Applications of the Derivative: Related Rates Sharon Rose13.The Differential Naci John

13.1 Definition13.2 Application of the Differential Comparison of x and dx

14.Derivatives of Trigonometric Functions Sharon Rose14.1 Elementary Properties14.2 Definition14.3 Graphs of Trigonometric Functions14.4 Applications

15.Derivatives of Inverse Trigonometric Functions Sharon Rose15.1 Elementary Properties15.2 Definition15.3 Graphs of Inverse Trigonometric Functions15.4 Applications

16.Derivatives of Logarithmic and Exponential Functions Sharon Rose16.1 Elementary Properties16.2 Definition16.3 Graphs of Logarithmic and Exponential Functions16.4 Applications

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17.Derivatives of Hyperbolic Functions Sharon Rose17.1 Elementary Properties17.2 Definition17.3 Graphs of Hyperbolic Functions17.4 Applications

18.Solution of Equations Naci John18.1Newtons Method of Approximation18.2Newton-Raphson Law

19.Transcendental Curve Tracing Naci John19.1 Logarithmic and Exponential Functions

20.Parametric Equations Sharon Rose21.Partial Differentiation Naci John