# Read PDF Complex Variables II Essentials: v. 2

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Financial mathematics is applied to areas of financial economics important in actuarial applications. Emphasis is placed on topics included in the financial economics portion of the Society of Actuaries' Financial Mathematics exam. This course covers special undergraduate topics in mathematics which are not taught elsewhere in the department. This course may be repeated for credit when topic is different. Prerequisites: Departmental approval. This course is intended as a chance for mathematics majors to enhance their skills in mathematical problem solving.

Students will learn how to use different techniques to tackle different types of problems ranging from the Calculus to advanced level math courses. In addition to learning problem solving techniques, students will be encouraged to discuss the best methods for solving problems efficiently. This course is highly recommended for math majors who are planning to apply for graduate school.

This course is an introduction to the theory of functions of a complex variable with basic techniques and some applications. Topics include complex numbers and the extended complex plane, elementary functions of a complex variable, differentiation, conformal mappings, contour integration, Cauchy's theorem, Cauchy's formula, Taylor and Laurent series, and residue theory. This course is an introduction to elementary partial differential equations, with applications to physics and engineering. Heat conduction, diffusion processes, wave phenomenon, and potential theory are explored by means of Fourier analysis.

This course is an introduction to transform analysis based on the theory of Fourier and Laplace integrals. Topics include contour integration, inverse formulas, convolution methods, with application to mathematical analysis, differential equations and linear systems. Topics include a complete overview of Hilbert's axioms connection, order, parallels, congruence, continuity , convex geometry convex hull, extreme points, linear programming , and projective geometry collineation, coordination, the Main Theorem, affine spaces.

This course presents a rigorous introduction to the elements of topology. Topics include a study of metric spaces, separation axioms, topological spaces, and topological properties of point sets and mappings. This course is a first introduction to the ideas behind Algebraic Geometry: Nullstellensatz, the definition of varieties, and mappings between them. To Illustrate key ideas and motivate theorems, this course focuses its attention on concrete examples, often making use of mathematical software for visualization.

Additionally, students will learn about computational techniques and how to use them. Starting with multi-variable calculus, this course will develop the theme of invariants attached to the geometry of curves and surfaces. The various notations of curvature of surfaces are related to curvature and torsion of curves. The contrast between local and global phenomena is also emphasized.

Visualization of ideas with mathematical software will be regularly present. This course is a continuation of MATH Topics include groups, rings, and fields, with applications to geometric constructability and solvability by radicals. This is a proof-based course of linear algebra topics chosen from vector spaces, linear transformations, determinants, matrices, equivalence relations, canonical forms, inner product spaces, linear functional, and applications.

Topics include Riemann integration of a single-variable function; continuity, differentiation and integration of multivariable functions; the mean value theorem; the implicit and inverse function theorems; Green's theorem; and the convergence of sequences and series of functions. Students will complete a major mathematical project and will communicate its results in oral and written form.

Students will also take comprehensive test from the Mathematics core courses. This course is designed to give students experience in research not normally covered within standard courses. Research projects will vary according to student interest and faculty availability. Students will complete a major mathematical research project communicating its results both in oral and written forms to the department faculty and students. MATH - Intermediate Algebra A study of the real number system, equations, inequalities and its applications, graphs of equations and inequalities, exponents and polynomials, factoring and its applications, rational expressions and its applications, systems of linear equations and inequalities, roots and radicals, quadratic equations.

MATH - Contemporary Mathematics Topics include voting methods, apportionment methods, financial mathematics, mathematical logic, graph theory, statistics, and probability with an emphasis on problem solving and critical thinking. MATH - Elementary Statistical Methods This course provides an elementary overview of the nature and uses of descriptive statistics, inferential statistics, and probability.

MATH - Intro to Biostatistics Topics include introduction to biostatistics; biological and health studies and designs; probability and statistical inferences; one- and two-sample inferences for means and proportions; one-way ANOVA and nonparametric procedures. MATH - Fund of Mathematics I This course is designed for students seeking teacher certification from early childhood through eighth grade.

Prerequisites: College Ready TSI status in mathematics and admission to the honors program MATH - College Algebra Topics include polynomial functions, rational functions, exponential functions, logarithmic functions, and matrices. MATH - Discrete Mathematics This course addresses mathematical topics readily used in computer science, including logic, mathematical proof, counting techniques, functions and relations, an introduction to computability, and the Church-Turing thesis. MATH - Linear Algebra Topics include systems of linear equations, matrices and their algebraic properties, determinants, vectors, Euclidean n-space, linear transformations and their matrix representations, vector spaces, eigenvalues and eigenvectors, and applications to the sciences and business.

MATH - Precalculus Topics include trigonometric functions, applications, graphs, equations, and identities; inverse trigonometric functions; vectors; sequences and series; the Binomial Theorem; conic sections; and parametric and polar equations. MATH - Calculus I Topics include limits, derivatives, antiderivatives, and definite integrals of algebraic and transcendental functions. MATH - Calculus II Topics include methods of integration, applications of definite integrals, parameterized curves, integration in polar coordinates, and infinite sequences and series.

MATH - Diff Equations This course studies first-order and linear second-order differential equations, Laplace transforms, power series solutions, and first order linear systems.

MATH - Linear Optimization The course covers basic theory of linear priming, an introduction to the simplex method path-following interior-point methods, and applications of linear programming. MATH - Numerical Methods This course studies the numerical solutions to various problems occurring in engineering, the sciences, and mathematics. MATH - Intro to Math Proof This course will prepare the student for advanced mathematics courses that require the writing of proofs.

MATH - Applied Discrete Mathematics Topics include applications of recurrence relations, advanced combinatorics, relations, graph theory, Boolean algebra, and modeling computation.

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MATH - Number Theory Topics include the binomial theorem, divisibility, the extended Euclidean algorithm, Diophantine equations, primes, congruences, Euler's Theorem, multiplicative functions, the Fibonacci sequence, Pythagorean triples, continued fractions, and applications to cryptology. MATH - Actuarial Stat Estimates Statistical tools used for the construction and evaluation of actuarial models are covered in this course.

MATH - Actuarial Financial Math Financial mathematics is applied to areas of financial economics important in actuarial applications. MATH - Special Topics in Math This course covers special undergraduate topics in mathematics which are not taught elsewhere in the department. MATH - Math Problem Solving This course is intended as a chance for mathematics majors to enhance their skills in mathematical problem solving.

MATH - Complex Variables This course is an introduction to the theory of functions of a complex variable with basic techniques and some applications. MATH - Boundary Value Problems This course is an introduction to elementary partial differential equations, with applications to physics and engineering. MATH - Modern Geometry II Topics include a complete overview of Hilbert's axioms connection, order, parallels, congruence, continuity , convex geometry convex hull, extreme points, linear programming , and projective geometry collineation, coordination, the Main Theorem, affine spaces.

MATH - Algebraic Geometry This course is a first introduction to the ideas behind Algebraic Geometry: Nullstellensatz, the definition of varieties, and mappings between them. MATH - Diff Geometry Starting with multi-variable calculus, this course will develop the theme of invariants attached to the geometry of curves and surfaces.

MATH - Adv Linear Algebra This is a proof-based course of linear algebra topics chosen from vector spaces, linear transformations, determinants, matrices, equivalence relations, canonical forms, inner product spaces, linear functional, and applications. MATH - Math Project Students will complete a major mathematical project and will communicate its results in oral and written form. MATH - Research Experience in Math This course is designed to give students experience in research not normally covered within standard courses.

Jump to Top. Plant Modeling for Control Design. High Performance Computing. Section 5: Functions: Defining, Evaluating and Graphing.

Mod-01 Lec-02 Analytic functions of a complex variable (Part II)

The remainder of the section covers evaluating functions, solving equations with functions, and graphing functions. Defining and Clearing a Function in Maple. Maple requires special notation when defining a function , as opposed to defining an expression. Take note of the syntax here. The first input fails to define the desired function because of the assignment to the symbol. In general, this kind of assignment should be avoided in Maple. The second input creates an expression , not a function. Below is a comparison of an expression and a function. Note the difference in syntax and how Maple returns the output for each.

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This is the expression,. Generally, functions require an arrow when typed in from the keyboard. When created this way, the Maple echo should also have an arrow in its output. Always check the output for the arrow to confirm that you have in fact defined a function. Exercise 5. In the workspace below, enter the function. Student Workspace 5. Answer 5. Once you have defined a function, Maple will remember that function during your entire working session. If you want to overwrite the function with a new definition, you simply retype the definition.

We can confirm the current value for the function :.

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It's always a good idea to clear your functions when you start a new problem. If the following three commands. The Maple commands. In fact, it is generally not wise to assign to the symbol. To create the function and evaluate it at , use the syntax. Evaluating a Function. Once a function has been defined, you can evaluate it at various values or literal expressions using function notation.

It's always a good idea to clear the function name first before entering a new function. Now, assign a new function to f. For example:. For example, the Newton or difference quotient for this function would be. Given the second function. Don't forget the arrow notation! For :. To simplify the result:. Solving Equations Involving Functions. Once your function is defined, you can solve equations containing this function either exactly or approximately. If the function is.