Calculus 1 for Life Sciences

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

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

• find limits involving algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions by inspection as well as by limit laws
• calculate infinite limits and limits at infinity
• apply L'Hôpital's rule to evaluating limits of the types: 0/0, infinity/infinity, infinity - infinity, 0⁰,  infinity⁰, 1^infinity
• determine intervals of continuity for a given function
• calculate a derivative from the definition
• differentiate algebraic, trigonometric and inverse trigonometric functions as well as exponential  and logarithmic functions of any base using differentiation formulas and the chain rule
• differentiate functions by logarithmic differentiation
• apply the above differentiation methods to problems involving implicit functions, curve sketching, applied extrema, related rates, and growth and decay problems
• use differentials to estimate the value of a function in the neighbourhood of a given point, and to estimate errors
• apply derivatives to investigate the stability of recursive sequences
• interpret and solve optimisation problems
• sketch graphs of functions including rational, trigonometric, logarithmic and exponential functions, identifying intercepts, asymptotes, extrema, intervals of increase and decrease, and concavity
• compute simple antiderivatives, and apply to first order differential equations
• recognise and apply the Mean Value Theorem  and  the Intermediate Value Theorem