Math 105 introduces integral calculus for commerce and social sciences students at UBC. Building on the derivatives and optimization you learned in Math 104, you'll now work with integrals to calculate total cost, consumer surplus, present value, and more. Integrals let you accumulate marginal quantities—turning marginal cost into total cost, or revenue rate into total revenue. It's a powerful tool for business analysis, but like all calculus, it requires practice, conceptual understanding, and strategic problem-solving.
What is covered in UBC Math 105?
Math 105 introduces integral calculus with applications to commerce and 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 commerce applications)
- Applications in commerce: Total cost from marginal cost, consumer and producer surplus, present and future value
- Differential equations: First-order equations including exponential growth models and equilibrium analysis
- Functions of several variables: Partial derivatives and optimization with multiple variables
- Constrained optimization: Using Lagrange multipliers to optimize with constraints (e.g., budget limits)
- Probability and statistics basics: Using integrals to calculate probabilities and expectations
Math 105 is required for many commerce, economics, and business programs and is typically paired with Math 104 as a two-course sequence.
Common challenges students face in Math 105
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.
Business 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 105
Our tutors specialize in calculus for commerce and understand both the math and the business applications.
Step-by-step integration strategies
We teach you how to recognize which integration technique to use and how to set up integrals for business problems. You'll learn substitution, integration by parts, and when to use approximation methods.
Contextual problem solving
We walk you through applications: calculating consumer surplus, finding present value, solving differential equations for equilibrium models, and optimizing with constraints.
Partial derivatives and optimization
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 105 exam and midterm preparation
Math 105 typically includes two midterms and a final exam. Here's how we prepare you:
Practice with commerce 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 105 tutoring?
First-year specialization
We focus on UBC's first-year math courses, including calculus for commerce. Our tutors have helped hundreds of Math 105 students succeed.
Experience with UBC curricula
We know the textbook, the types of problems UBC professors emphasize, and the exam formats. We tailor our sessions to UBC's specific Math 105 curriculum.
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 105 topics with business examples—perfect for reviewing before exams.
Frequently Asked Questions
What's the difference between Math 105 and Math 101?
Math 105 is for commerce and social sciences students, with applications like consumer surplus, present value, and constrained optimization. Math 101 is for physical sciences and engineering, focusing on physics applications like work, volumes of revolution, and mechanics. The core integration techniques are similar, but the applications differ.
Can I take Math 101 instead of Math 105?
Usually, yes—check with your program. Math 101 is often accepted as equivalent to Math 105, but its applications are more physics-focused. If you're a commerce or economics major, Math 105's business context will be more relevant.
Do I need Math 104 to take Math 105?
Yes. Math 105 assumes you're comfortable with derivatives, exponential functions, and the Fundamental Theorem of Calculus from Math 104. If you skipped Math 104 (e.g., through AP credit), review differentiation before starting Math 105.
How much do Lagrange multipliers count on the final?
Constrained optimization with Lagrange multipliers typically makes up 10-20% of the Math 105 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 105 final?
Start at least two weeks before the exam. The final is cumulative, covering everything from basic antiderivatives to constrained optimization and differential equations. You need time to practice integration techniques and business applications thoroughly.