Second course in calculus and analytic geometry. Applications of Definite Integral; Hyperbolic Functions, Inverse Trigonometric and Hyperbolic Functions; Techniques of Integration; Improper Integrals: Topics of Analytical Geometry; Polar Coordinates and Parametric Equations.
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Basic concepts and techniques of linear algebra; includes system of linear equations, matrices and inverses, determinants, and a glimpse at vector spaces, eigenvalues and eigenvectors, Markov processes.
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Covers basic calculus and analytic geometry. Coordinates, Graphs and Lines; Functions and Limits; Differentiations; Application of Differentiation; Integration; Logarithmic and Exponential Functions.
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Topics includes sets, real number system, algebraic expressions, systems of equations, functions and relations, quadratic functions, synthetic division, the zeros of a polynomial function, exponential and logarithmic functions, trigonometric functions, graphs of trigonometric functions, analytic trigonometry, additional applications of trigonometry, mathematical induction, the binomial theorem, sequences. Prerequisite: High School Mathematics.
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Engineering mathematics applies mathematical methods and techniques to solve practical problems in engineering. It integrates advanced concepts from calculus, linear algebra, differential equations, probability, and statistics to model and analyze complex systems. Key areas include optimization, numerical methods, Fourier analysis, and complex variables, which are essential for designing and analyzing structures, systems, and processes. Engineering mathematics is a foundational tool for fields like mechanical, electrical, civil, and aerospace engineering, enabling engineers to develop efficient solutions and innovations.
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Calculus 3, also known as Multivariable Calculus, extends the concepts of single-variable calculus to functions of multiple variables. It focuses on topics like partial derivatives, multiple integrals, and vector calculus. Key concepts include gradient, divergence, curl, and Green's, Stokes', and Divergence theorems, which help analyze physical phenomena like fluid flow and electromagnetic fields. This course is essential for advanced applications in physics, engineering, and computer graphics, providing tools for solving problems in three-dimensional space and beyond.
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Probabilities and statistics are branches of mathematics that deal with data analysis and inference. Probability theory focuses on predicting the likelihood of future events based on certain assumptions. It uses models like probability distributions to describe how likely an event is to occur. Statistics, meanwhile, deals with the collection, analysis, interpretation, presentation, and organization of data. It helps in making sense of complex data sets and drawing conclusions about larger populations based on sample data. Both fields are essential for data-driven decision making in various disciplines such as finance, science, engineering, and social sciences, enabling professionals to assess risk, test hypotheses, and make informed decisions based on numerical data.
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