Credit: (4-2)5 

Content: Functions. Limits and continuity. Derivatives. Applications. Extreme values, the Mean Value Theorem and its applications, graphing. The definite integral. The indefinite integral. Logarithmic, exponential, inverse trigonometric functions and their derivatives. L'Hopital's rule. Techniques of integration. Improper integrals. Applications of the integral. Parametric curves and polar coordinates: Area and arclength. 

Goals: Calculus was first discovered to meet the needs of the scientists of the sixteenth and seventeenth centuries. Diferential calculus deals with the problem of calculating rates of change. It enables us to define slope of curves, to calculate velocities, accelerations of moving bodies and to predict the times when planets would be closest together or farthest apart. Integral calculus deals with the problem of determining a function from information about its rate of change. It enables us to calculate the future location of a body from its present position, to find the areas of irregular regions in the plane, to measure the lengths of curves, and to find the volumes and masses of arbitrary solids. The goal of this course is to present a modern view of calculus enhanced by the use of technology.

Course Outline: 

    Sections Covered and Comments

    P.1-P.5 Quick Review 
    1.2. Limits of Functions, 
    1.3. Limits at Infinity and Infinite Limits, 
    1.4. Continuity (note to continuous extension and  example 12. Explore(A.S.)), 
    1.5. The Formal Definition of Limit (one polynomial and one rational function as examples)
    2.1. Tangent Lines and Their Slopes, 
    2.2. The Derivative (note to singular points), 
    2.3. Differentiation Rules (Mathematical Induction, on page 108,(A.S.)), 
    2.4. Derivatives of Trigonometric Functions, 
    2.5. Chain Rule (omit explore)
    2.6. Using Derivatives (omit example3 and the rest of the section), 
    5.1. The Mean Value Theorem (note to Definition of Critical Point on page 130), 
    5.2. Increasing and Decreasing Functions (upto First Derivative Test)(note to Definition of  Increasing-Decreasing Functions “<“ is used) 
    2.7. Higher Order Derivatives (omit examples1 and 3)
    2.8. Implicit Differentiation, 
    4.1. Inverse Functions, 
    4.2. Exponential and Logarithmic Functions, 
    4.3. The Natural Logarithm and Exponential (examples 8 and 9 are important)
    4.5. The Inverse Trigonometric Functions (omit example7)
    4.6. Hyperbolic Functions (omit Inverse Hyperbolic Functions), 
    3.2. Related Rates, 
    3.3. Extreme Values, 
    3.4. Extreme Value Problems
    3.5. Linear Approximations (omit example8), 
    5.2. Increasing Decreasing Functions (start with FIRST Derivative Test), 
    5.3. Concavity and Inflections (note to Definition), 
    5.4. Sketching the Graph of a Function
    5.4. Sketching the Graph of a Function (note to  examples 6,7,8 and 9) 
    5.5. Indeterminate Forms and l’Hospital’s Rules
    2.9. Antiderivatives and Initial Value Problems (omit Differential Equations and Initial Value Problems) 
    6.1. Sums and Sigma Notations (A.S.) 
    6.2. Areas and Limits of Sums (example1(A.S.).  Omit explore), 
    6.3. The Definite Integral (examples1 and 2 (A.S.). Omit explore)
    6.4. Properties of Definite Integral (note to Integral of Piecewise Continuous Function), 
    6.5. The Fundamental Theorem of Calculus, 
    6.6. The Method of Substitution, 
    6.7. Areas of Plane Regions (omit explore)
    7.1. Integration By Parts, 
    7.2. Inverse Substitutions (note to Completing Square and x=tan(O/2) Substitution), 
    7.3. Integrals of Rational Functions
    8.1. Volumes of Solids of Revolution, 
    8.2. Other Volumes by Slicing (A.S.)
    8.3. Arc Length and Surface Area (omit explore) 
    9.2. Parametric Curves, 
    9.3. Smooth Parametric Curves and Their Slopes (omit Tangents and Normals to Parametric Curves, on page 487, and the rest of the section)
R E V I E W

Suggested textbooks: Robert A.Adams; Calculus: A Complete Course, 3rd Edition, Addison-Wesley, 1995  

Reference Books: 

•    G.B. Thomas and R.Finney; Calculus and Analytic Geometry. Addison-Wesley Publishing Com. 1996.  
•    R.Ellis and D. Gulick; Calculus with Analytic Geometry, 5 th Edition, SCP, 1994  
•    M.Spivak; Calculus 3 rd Edition, Publish of Perish, Inc.

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