Table of Contents
MTH201: Multivariable Calculus
This course focuses on two basic applications: Differential Calculus and Integral Calculus. Under these, you will study different techniques and some Fundamental theorems of calculus in multiple dimensions. MTH201 Handouts pdf
MTH201 Handouts pdf
Course Category: Mathematics
Course Outline
Introduction to three-dimensional geometry. Limits, continuity and Partial Derivatives of Multivariable Function. Vectors. Directional derivative. Tangent Planes and Normal Lines to the Surfaces. Maxima And Minima of Functions of two variables. Applications of Extrema of Functions. Double Integration in rectangular and polar coordinates. Vector-Valued Functions. Integration of Exact differentials. Line integrals. Greens Theorem and its application. Divergence and Curl of a vector. Scalar Fields, Higher Order Derivative & Leibniz Theorem, Taylor and Maclaurin Series and Numerical Integration. MTH201 Handouts pdf
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MTH201 HANDOUTS
MTH201: Multivariable Calculus
System of Reference Axes
Before introducing the concept of the reference axis system, we will recall the concept of the real line and locate some points on the real line as shown in the figure below, also remember that the real number system consists of both rational and irrational numbers, which we can write the set of real numbers as the union rational and irrational numbers.
The intersection of two Planes
If two planes are not parallel, then they intersect and their point of intersection is a straight line. Thus, two non-parallel planes represent a line given by two simultaneous linear equations in x, y, and z, and are known as nonsymmetric forms of the equations of the line.
Rectangular coordinates for three dimensions:
Because you know that the position of any point in three dimensions can be obtained by three mutually perpendicular lines known as the x, y, and z axes and also shown in the figure below. These coordinate axes are known as the rectangular coordinate system.
