What are the Core Subjects for Mechanical Engineers ?
Introduction to Mechanical Engineering or Basic Mechanical Engineering
Different types of energy sources (both conventional and non-conventional), boilers or steam generators and their integral parts ( mountings and accessories), Turbines (Impulse and reaction), IC engines, some basic automotive knowledge, a brief but important knowledge about pumps, compressors , fans and blowers, basic thermodynamics with refrigeration and air conditioning, simple laws of mechanics.
Mechanical Drawing

Introduction to mandatory instruments required for the drawing, Different types of projections, Orthographic drawings, Isometric views, drawing of sections of different machine parts, auxiliary views etc.
Thermodynamics

Very important subject for mechanical engineers. Discusses the different aspects of thermal physics. Thermal engineering is another named used for Mecha. Engineers. Thermodynamics includes The three important laws of thermodynamics, basic concepts and properties of gases and vapors, systems, boundaries, thermodynamic cycles and processes, enthalpy, entropy and internal energy, refrigeration system, thermal comfort, psychrometry and combustion of engines.
Engineering Mechanics

It is divided into two main parts : statics and dynamics. Statics deals with forces in static and rigid bodies. It also discusses friction, moment of inertia ( both masses and areas), analysis of forces in truss and friction in stationary bodies.
Dynamics has the kinetics and kinematics. It mainly discusses the Newtonian physics. Friction in moving bodies, energy and forces in bodies having linear and rotational motion, impulse-momentum etc.
Mechanics of Solids or Solid Mechanics

It deals with stress analysis of different load carrying members. Discusses Beams and Columns and equation of torsion.
Heat Transfer

It discusses different theories of conduction, radiation and convection heat transfer.
Fluid Mechanics

Basic hydrostatic equations, compressible and incompressible flows , Velocity , momentum, continuity equation. Flow metering, boundary conditions etc.
Machine Design

Mechanics of Machinery
Mechanisms, Velocity , balancing of the rotating and reciprocating parts, vibration theories etc.
Instrumentation and Measurement
Internal Combustion Engines (IC engines)

Basic engines types, operations, cycles, SI and CI engines classifications. Performance measurements.
Power Plant Engineering

Discusses about power plant loads, fuels, operations, maintenance, cycles, turbines. generation of power.
Refrigeration and building mechanical systems
Basic refrigeration theorems, COP, different refrigeration systems, basic elements of refrigeration, cooling load calculation.
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Truely nice briefs on each subject, thermal engineering also be added..please!