Course Contents
Students should be able to work with functions represented in a variety of Ways: graphical, numerical, analytical, or verbal. They should understand the Connections among these representations. Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems. Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of a rate of change and should be able to use integrals to solve a variety of problems
Course Synopsis
Implementation and study of different functions, their limits, continuity derivatives, Anti derivatives, integrals and also the study of the behaviour of functions
Course Learning Outcomes
After completion of this course students will be able to:
• Discuss properties of real numbers.
• Calculate the derivatives and integrals of functions using different techniques
• Apply different theorems i.e M.V.T. , Roll s theorem, G.M.V.T.
• See the behaviour of surfaces as well as students must be able to identify the different equations ellipse, parabola, and hyperbola.
An Introduction to Limits
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Properties of Limits. Techniques of Limit Computation
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Continuity of Functions
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Slope of a Curve, Velocity, and Rates of Change
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Introduction to the Derivative of a Function
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Techniques of Differentiation
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The Product and Quotient Rules for Derivatives of Functions
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Finding Derivatives of Trigonometric Functions
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Discussion of the Chain Rule for Derivatives of Functions
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Increasing/Decreasing and Concavity of Functions
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A BRIEF Discussion of Rolle's Theorem and Mean-Value Theorem.
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The First Derivative Test for Increasing and Decreasing
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The Second Derivative Test for Concavity of Functions
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How to Sketch Graphs of Functions
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An Introduction to the Indefinite Integral
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The Evaluation of Definite Integrals
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Finding Area Between Two Curves
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Volume of Solids By Cylindrical Shells Method
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Book Title : Advanced Engineering Mathematics
Author : E. Kreyszig
Edition : 7th edition
Publisher : John Wiley
Book Title : Applied Numerical Analysis
Author : C. F. Gerald
Edition : 2nd Edition
Publisher : Addison-Wesley 1978
Book Title : Mathematical Method for Physicists
Author : G. Arfken
Edition : 2nd edition
Publisher : Academic Press 197
Book Title : Calculus & Analytic Geometry
Author : M.Amin and S.M Yousaf
Edition :
Publisher :
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