Mathematics I (MTH117) — Notes, Syllabus & Past Questions

Basic calculus, algebra, and analytical geometry concepts required for computing applications.

Core Course10 Chapters
Chapter 1Past Questions

Function of One Variable

Four ways of representing a function, Linear mathematical model, Polynomial, Rational, Trigonometric, Exponential and Logarithmic functions, Combination of functions.

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Chapter 2Past Questions

Limits and Continuity

Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes.

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Chapter 3Past Questions

Derivatives

Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L'Hospital rule.

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Chapter 4Past Questions

Applications of Derivatives

Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton's method.

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Chapter 5Past Questions

Antiderivatives

Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The Fundamental theorem of calculus, Improper integrals.

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Chapter 6Past Questions

Applications of Antiderivatives

Areas between the curves, Volumes of cylindrical cells, Approximate Integrations, Arc length, Area of surface of revolution.

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Chapter 7Past Questions

Ordinary Differential Equations

Introduction, Introduction to first order equations Separable equations, Linear equations, Second order linear differential equations, Non homogeneous linear equations.

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Chapter 8Past Questions

Infinite Sequence and Series

Infinite sequence and series, Convergence tests and power series, Taylor's and Maclaurin's series.

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Chapter 9Past Questions

Plane and Space Vectors

Introduction, Applications, Dot product and cross Product, Equations of lines and Planes, Derivative and integrals of vector functions, Arc length and curvature, Normal and binormal vectors.

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Chapter 10Past Questions

Partial Derivatives and Multiple Integrals

Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values, Multiple integrals.

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