SFU MATH 151 Calculus I: Syllabus, Topics and Practice

MATH 151 is Calculus I at Simon Fraser University, the first calculus course for students heading into mathematics, physics, chemistry, computing science and engineering. It is a 3-unit course that builds differential calculus from the ground up and adds a few extras, such as Newton's method, a first taste of differential equations, and polar and parametric curves. This guide maps every MATH 151 topic to free practice so you can learn each idea by solving problems with instant feedback.

What SFU MATH 151 covers

The SFU academic calendar lists these topics for MATH 151: logarithmic and exponential functions, trigonometric functions and inverse functions; limits, continuity and derivatives; techniques of differentiation, including logarithmic and implicit differentiation; the Mean Value Theorem; applications of differentiation including extrema, curve sketching and Newton's method; an introduction to modelling with differential equations; and polar coordinates and parametric curves.

Compared with a typical Calculus 1, MATH 151 stops before integration. Definite integrals, the Fundamental Theorem of Calculus and integration techniques all wait for MATH 152. In exchange, it spends time on approximation (Newton's method) and on describing curves in new ways (polar and parametric).

MATH 151 topic map

MATH 150 vs MATH 151 vs MATH 154

Only one of these counts for credit. After MATH 151, continue to MATH 152 and then MATH 251.

Example problems at the MATH 151 level

1. Logarithmic differentiation. Differentiate y = x^x for x > 0. Take logs: \ln y = x \ln x. Differentiate both sides:

2. Newton's method. Approximate the root of f(x) = x^3 - 2x - 5 near x_0 = 2. Since f'(x) = 3x^2 - 2:

3. A polar curve. Convert r = 2\cos\theta to Cartesian form. Multiply by r: r^2 = 2r\cos\theta, so x^2 + y^2 = 2x, a circle of radius 1 centred at (1, 0).

How to do well in MATH 151

• Fix your precalculus first. The course opens with exponential, logarithmic and inverse functions. Gaps there slow down every later topic.
• Drill the rules until they are automatic. Short daily sets in practice on the power rule, product rule and chain rule free up exam time for applications.
• Check theorem hypotheses. Before you use the Mean Value Theorem, confirm continuity on the closed interval and differentiability inside it.
• Sketch before you compute. For curve sketching and Newton's method, a rough graph tells you where to look and whether an answer is reasonable.
• Use SFU's support. The calendar mentions the Calculus Workshop (Burnaby) and Math Open Lab (Surrey) for MATH 150 students, and they are a good place to ask questions.

Tip: when you convert between polar and Cartesian form, the identities x = r\cos\theta, y = r\sin\theta and x^2 + y^2 = r^2 do almost all the work.