Calculus 2 for Life Sciences

MATH 1223 is a second course in calculus.  Together with MATH 1123 it forms a science-based introduction to calculus providing the foundation for continued studies in biological or life sciences.

By the end of the course, students will be able to:

• compute finite Riemann sums and use to estimate area
• form limits of Riemann sums and write the corresponding definite integral
• recognize and apply the Fundamental Theorem of Calculus
• evaluate integrals involving exponential functions to any base
• evaluate integrals of rational functions
• evaluate integrals involving basic trigonometric functions and integrals whose solutions require inverse trigonometric functions
• choose an appropriate method and apply the following techniques to find antiderivatives and evaluate definite integrals:
• integration by parts
• completing the square for integrals involving quadratic expressions
• partial fractions
• apply integration to problems involving areas, volumes, arc length, velocity and acceleration
• be able to determine the convergence or divergence of improper integrals by the comparison test
• approximate a differentiable function by a Taylor polynomial, determine the remainder term, and compute the error in using the approximation
• solve first-order differential equations by the method of separation of variables; apply to growth and decay problems
• find equilibria of differential equations and determine their stability graphically and analytically
• describe the behavior of solutions of differential equations, starting from different initial conditions
• use systems of differential equations to describe biological systems with multiple interacting components
• solve systems of linear equations
• define matrices and perform algebraic operations on matrices
• define and use functions of two or more independent variables
• find limits of multi-variable functions and describe their continuity
• calculate partial derivatives and apply them to biological science problems