Download Applied Mathematics Lesson and Exercises and more Exercises Applied Mathematics in PDF only on Docsity!
📘 Lesson: Introduction to Applied
Mathematics
📖 What Is Applied Mathematics?
Applied Mathematics is the branch of mathematics that deals with mathematical methods and models used in real-world problems across science, engineering, business, economics, social sciences, and more. It differs from pure mathematics in that its goal is to solve practical problems rather than explore abstract theories.
In simple terms, applied mathematics takes tools from algebra, calculus, statistics, and linear algebra and applies them to real-life applications such as:
Predicting weather
Managing finances
Optimizing logistics
Engineering designs
Data science and AI
🎯 Learning Objectives
By the end of this lesson, you will be able to:
Understand the scope and importance of applied mathematics Translate real-world situations into mathematical models Solve real-life problems using appropriate mathematical methods Interpret solutions in context
🌐 Scope of Applied Mathematics
Applied math is used in virtually every field. Below are some areas where it's essential:
Field Application Example Engineering Designing bridges, circuits, or machinery Economics Forecasting supply and demand Physics Modeling motion and force Medicine Modeling the spread of diseases (epidemiology) Computer Science Cryptography, algorithms, machine learning Environmental Sci. Modeling climate change or pollution levels Business Cost optimization, profit maximization, data analysis
📖 Real-World Problem Solving with Examples
Example 1: Business — Profit Analysis
Problem: A company manufactures and sells gadgets. Each gadget costs $25 to produce. They sell them for $40 each. The company pays a fixed cost of $1,500 per month in rent, utilities, and salaries. How many gadgets must they sell to break even?
Solution:
Let:
x = number of gadgets Cost = Fixed Cost + Variable Cost = 1500+25x Revenue = 40x40x40x
Set Revenue = Cost to find the break-even point:
40x=1500+25x
Subtract 25x from both sides:
15x=
Divide by 15:
x=
✅ Answer: The car decelerates at 5 m/s².
📦 Example 5: Logistics — Container Packing
Problem: Each box measures 2 ft × 2 ft × 3 ft. A shipping container has internal dimensions of 20 ft × 8 ft × 8 ft. What is the maximum number of boxes that can be packed inside?
Solution:
Find the number of boxes that fit along each dimension:
Length: 20/2=
Width: 8/2=
Height: 8/3≈2 (only 2 boxes fully fit in height)
Total boxes:
10×4×2= 80
✅ Answer: The maximum number of boxes is 80.
Key Takeaway
Applied mathematics makes math meaningful. It’s not just about numbers—it's about using those numbers to make decisions, save resources, solve problems, and understand the world around us.
