MATH162 — Calculus II
Presents integration techniques, improper integrals, sequences, series, and applications including numerical methods and differential equations.
Learning Objectives & Matches
Compute volumes using a variety of methods
Perform computations and apply methods of numerical analysis to data.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Apply integration techniques including substitution, parts, and partial fractions
Explain design specifications to integration or test engineers.
Develop methods for integrating different products so they work properly together, such as customizing commercial databases to fit specific needs.
Design and implement data repositories to integrate data.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Apply theoretical expertise and innovation to create or apply new technology, such as adapting principles for applying computers to new uses.
Perform computations and apply methods of numerical analysis to data.
Update client and server applications responsible for integration and business logic.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Participate in network technology upgrade or expansion projects, including installation of hardware and software and integration testing.
Apply the change of variable theorem to integrals
Evaluate improper integrals and analyze convergence behavior
Compute areas between graphs of function
Create graphs, charts, or other visualizations to convey the results of data analysis using specialized software.
Use transcendental functions including exponential and logarithmic functions
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Analyze problems to develop solutions involving computer hardware and software.
Adapt statistical methods to solve specific problems in many fields, such as economics, biology, and engineering.
Perform computations and apply methods of numerical analysis to data.
Formulate mathematical or simulation models of problems, relating constants and variables, restrictions, alternatives, conflicting objectives, and their numerical parameters.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Write new functions or applications in programming languages to conduct analyses.
Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Solve first-order differential equations using analytical methods
Write description of the improper integral as a limit
Apply numerical methods for approximating integrals and solutions
Evaluate improper integrals
Analyze sequences and series for convergence and approximation
Derive formulas for the derivatives of such functions as arcsin(Q) and arctan(Q) by using the chain rule and the trigonometric identities
Model physical systems using differential equations and integration
Demonstrate knowledge of relationships between exponents and logarithms and their derivatives
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
Break systems into their components, assign numerical values to each component, and examine the mathematical relationships between them.
Mentor others on mathematical techniques.
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Examine theories, such as those of probability and inference, to discover mathematical bases for new or improved methods of obtaining and evaluating numerical data.
Conduct logical analyses of business, scientific, engineering, and other technical problems, formulating mathematical models of problems for solution by computers.
Propose solutions in engineering, the sciences, and other fields using mathematical theories and techniques.
Educate staff in the use of mathematical models.
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
Demonstrate the ability to perform integration by applying one of the following techniques: Powers of trigonometric functions, Trigonometric substitution, Algebraic substitution, Method of parts, Partial fractions for the linear and the quadratic case
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
Understand the development of the natural logarithmic function
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
Compute arc lengths of curves
Compute areas of surfaces of revolution