Best binary options graphs of trigonometric identities
Differentiation of the elementary functions, including trigonometric functions. Max-min problems, curve sketching. Functions of several variables, partial differentiation, constrained max-min. Definite and indefinite integrals. This course is not acceptable for substitute credit in any of the following degree programs: Vector spaces, matrix algebra, linear dependence, bases, linear transformations, bilinear and quadratic forms, inner products, eigenvalues, diagonalization; emphasis on proofs and theory.
Lectures three hours a week, tutorial one and a half hours a week. Linear transformations, kernel, range. Inner product spaces and orthogonality. Lectures three hours a week and tutorial one hour a week. Complex numbers including de Moivre's Theorem, and n-th roots.
Eigenvalues, diagonalization and applications. Use of illustrative examples related to business. Precludes additional credit for for, but is not an acceptable substitute for: Economic applications such as profit maximization, comparative statics, and the Leontief input-output model.
The practice of mathematical proof in elementary number theory and combinatorics. Material is illustrated through examples from computing. Use of implicit and inverse function theorems. Real number axioms, limits, continuous functions, differentiability, infinite series, uniform convergence, the Riemann integral.
Lectures three hours a week and one hour tutorial. Polar, cylindrical and spherical coordinates. Partial derivatives, gradients, extrema and Lagrange multipliers. Multiple integrals over rectangular and general regions. Polar coordinates, parametric equations. Indeterminate forms, sequences and series, Taylor's formula and series. Introduction to ring theory: Hermitian form, spectral theorem for normal operators, classical groups.
Linear transformations and matrices. Inner product spaces over R and C ; Orthonormal bases. Bilinear and quadratic forms; principal axis theorem. This course is intended for a general audience, and is available to B. Grade 12 Mathematics and second-year standing. First-order equations, linear second- and higher-order equations, linear systems, stability of second-order systems. Basic number theory and counting methods, algorithms for strings, trees and sequences.
Applications to DNA and protein sequencing problems. Analysis and complexity of algorithms. Also listed as CMPS Lectures three hours a week. Vector fields, differential forms and exterior algebra. Introduction to manifolds and tangent bundles. Applications such as differential equations and the calculus of variations. Intended for non-engineering students. Bessel and Legendre functions. This course may not be used to meet the level course requirements in any General or Honours program in Mathematics and Statistics.
Direct methods of solving a system of linear equations. Power method and deflation techniques of approximation. Emphasis is primarily on computational aspects. Polynomials, unique factorization domains. Field extensions, finite fields. Geometric constructions - three famous problems: Precludes additional credit for MATH Poincare disk model of the hyperbolic plane. Development of the systems of natural numbers and the real numbers. Axiom of choice, Zorn's lemma, well-ordering.
Systems of ordinary differential equations of first order; matrix methods. Existence and uniqueness theorems. Nonlinear autonomous systems of order 2; qualitative theory. Numerical solutions of ordinary differential equations. Fourier series and Fourier transforms, solutions of partial differential equations of mathematical physics, boundary value problems, applications. This course may be taken for credit as a level Honours Mathematics course, by students in any Honours program in the School of Mathematics and Statistics.
Computational methods, including function evaluation, interpolation, solution of linear equations, root finding, integration, solution of differential equations, Fourier series and Monte Carlo methods. Lectures three hours a week, laboratory one hour a week. Network flow problems and the network simplex method. MATH , or permission of the School. The course includes examination of existing software systems, e.
The topics include probabilities, odds, house advantages, variance and risks, optimal strategies, random walks and gambler's ruin, and gaming revenue estimation. They have almost completely replaced slide rules in traditional applications, and are widely used in both education and professional settings.
In certain contexts such as higher education, scientific calculators have been superseded by graphing calculators , which offer a superset of scientific calculator functionality along with the ability to graph input data and write and store programs for the device. There is also some overlap with the financial calculator market.
Modern scientific calculators generally have many more features than a standard four or five-function calculator, and the feature set differs between manufacturers and models; however, the defining features of a scientific calculator include:. While most scientific models have traditionally used a single-line display similar to traditional pocket calculators, many of them have more digits 10 to 12 , sometimes with extra digits for the floating point exponent. A few have multi-line displays, with some models from Hewlett-Packard , Texas Instruments , Casio , Sharp , and Canon using dot matrix displays similar to those found on graphing calculators.
Scientific calculators are used widely in situations that require quick access to certain mathematical functions, especially those that were once looked up in mathematical tables, such as trigonometric functions or logarithms. They are also used for calculations of very large or very small numbers, as in some aspects of astronomy , physics , and chemistry. They are very often required for math classes from the junior high school level through college, and are generally either permitted or required on many standardized tests covering math and science subjects; as a result, many are sold into educational markets to cover this demand, and some high-end models include features making it easier to translate a problem on a textbook page into calculator input, e.
The first scientific calculator that included all of the basic ideas above was the programmable Hewlett-Packard HPA ,  released in , though the Wang LOCI-2 and the Mathatronics Mathatron had some features later identified with scientific calculator designs.
The HP series was built entirely from discrete transistor logic with no integrated circuits , and was one of the first uses of the CORDIC algorithm for trigonometric computation in a personal computing device, as well as the first calculator based on Reverse Polish Notation RPN entry.
HP became closely identified with RPN calculators from then on, and even today some of their high-end calculators particularly the long-lived HPC financial calculator and the HP series of graphing calculators still offer RPN as their default input mode due to having garnered a very large following. The HP , introduced on February 1, , was Hewlett-Packard's first pocket calculator and the world's first handheld scientific calculator.
Texas Instruments TI , after the introduction of several units with scientific notation, came out with a handheld scientific calculator on January 15, , in the form of the SR Casio, Canon and Sharp have also been major players, with Casio's fx series beginning with the Casio fx-1 in  being a very common brand, used particularly in schools.
Casio is also a major player in the graphing calculator market, and was the first company to produce one Casio fxG.