SFU Math 158 is Calculus II for social sciences students—the continuation of Math 157. Building on the derivatives and optimization you learned in Math 157, you'll now work with integrals to calculate total cost, consumer surplus, present value, and cumulative change. You'll also explore functions of several variables, which let you model economic systems with multiple inputs (labor and capital, price and quantity). Integrals and multivariable functions are powerful tools for economics, business, and social sciences—and Math 158 teaches you how to use them effectively.
What is covered in SFU Math 158?
Math 158 introduces integral calculus and multivariable calculus with applications to social sciences. Topics include:
- Antiderivatives and indefinite integrals: Reversing differentiation to find original functions
- The definite integral: Riemann sums, area under curves, and the Fundamental Theorem of Calculus
- Integration techniques: Substitution and basic integration methods (tailored to social sciences applications)
- Applications in social sciences: Total cost from marginal cost, consumer and producer surplus, present and future value
- Functions of several variables: Partial derivatives and optimization with multiple variables (e.g., production functions)
- Constrained optimization: Using Lagrange multipliers to optimize with constraints (budget limits, resource allocation)
- Probability basics: Using integrals to calculate probabilities and expected values in social contexts
- Differential equations (introduction): First-order equations including exponential growth and equilibrium models
Math 158 completes the calculus sequence for social sciences students and is required for many economics, business, and social sciences programs.
Common challenges students face in Math 158
Integration is harder than differentiation
Derivatives follow clear rules. Integration requires recognizing patterns and choosing the right technique. Not every function has a simple antiderivative, and choosing wrong wastes time on exams.
Economic applications feel abstract
You're asked to integrate functions representing marginal cost, revenue rates, or demand curves. If you don't understand the economics, setting up integrals correctly is difficult.
Functions of several variables
Partial derivatives and optimization with multiple variables (like cost depending on labor and capital) add complexity. The notation alone—∂f/∂x—can be confusing at first.
Constrained optimization with Lagrange multipliers
This technique is powerful but abstract. You need to set up the Lagrangian, take partial derivatives, and solve systems of equations—all while understanding what the constraint represents economically.
How Learn4Less helps you succeed in Math 158
Our tutors specialize in calculus for social sciences and understand both the math and the applications.
Step-by-step integration strategies
We teach you how to recognize which integration technique to use and how to set up integrals for economic problems. You'll learn substitution and integration methods efficiently and confidently.
Contextual problem solving
We walk you through applications: calculating consumer surplus, finding present value, and optimizing with constraints. You'll understand not just the math but the economic meaning.
Partial derivatives and Lagrange multipliers
We demystify functions of several variables. You'll learn how to take partial derivatives, interpret them economically, and use Lagrange multipliers to solve constrained optimization problems.
Math 158 exam and midterm preparation
Math 158 typically has midterms and a final exam. Here's how we prepare you:
Practice with social sciences applications
We focus on the types of problems that appear most often: consumer surplus, total cost from marginal cost, present value calculations, and constrained optimization.
Past exam practice
We work through previous years' exams so you're familiar with question formats, time constraints, and how partial credit is awarded.
Concept interpretation
Exams ask you to explain what your integral represents: "What does ∫MC(q)dq from 0 to 100 mean economically?" We drill you on these conceptual questions.
Why choose Learn4Less for Math 158 tutoring?
First-year specialization
We focus on SFU's first-year calculus courses, including social sciences calculus. Our tutors have helped hundreds of Math 158 students succeed.
Experience with SFU curricula
We know SFU's Math 158 syllabus, typical textbooks, and exam formats. We tailor our sessions to what SFU professors emphasize: economic applications and multivariable optimization.
Flexible learning options
Choose in-person tutoring near UBC or online sessions. Need help before a specific midterm? Book a targeted prep session. Want consistent support? Weekly tutoring keeps you on track.
Video study packages
Prefer self-paced learning? Our video packages cover key Math 158 topics with economic examples—perfect for reviewing before exams.
Frequently Asked Questions
What's the difference between Math 158 and Math 152?
Math 158 is for social sciences students, with applications like consumer surplus, present value, and constrained optimization. Math 152 is for physical sciences and engineering, focusing on physics applications like work and volumes of revolution. The core integration techniques are similar, but the applications differ.
Do I need Math 157 to take Math 158?
Yes. Math 158 assumes you're comfortable with derivatives, exponential functions, and the Fundamental Theorem of Calculus from Math 157. If you skipped Math 157 (e.g., through AP credit), review differentiation before starting Math 158.
Can I take Math 152 instead of Math 158?
Check your program requirements. Math 152 is often accepted as equivalent, but its applications are more physics-focused. If you're an economics or business major, Math 158's economic context will be more relevant.
How much do Lagrange multipliers count on the final?
Constrained optimization with Lagrange multipliers typically makes up 15-25% of the Math 158 final exam. It's a key topic in the second half of the course, so don't neglect it.
When should I start studying for the Math 158 final?
Start at least two weeks before the exam. The final is cumulative, covering everything from basic antiderivatives to constrained optimization and functions of several variables. You need time to practice integration techniques and economic applications thoroughly.